I'm not able to answer the full question but I can explain Domitian's actions and their results. Hopefully someone else can build on that to provide a fuller answer.
Domitian's financial policies included the following (Southern 1997, p. 53):

• Canceling debts to the treasury.
• Refusing inheritances that would leave children without money.
• Increasing expenditure.
• Overhauling the mint (by ceasing bronze coin production and improving silver and gold varieties).
• Lavish building programs.
• Pay rise for the army.

After the year 85 a debasement of fine metals occurred, likely due to a crisis of some sort. Domitian refused to devalue coins further than they already had been, a step that would be taken by later emperors, which led to financial issues during his reign. (Southern 1997, p. 62). His large expenditures on extensive building programs and a massive pay-rise for the army left state finances strained even further. The managing of finances was a critical part of his reign, and he was willing to spend, spend, spend, whereas most other emperors were more conservative in their approach and tried to squeeze more money out of the population and spent less of it.
Domitian, unlike most all other emperors, had a very hands on approach to governmental matters. He micro-managed a lot of aspects that were usually just left to the devices of specific officials. He was big on rules and regulations and under his rule there was less corruption and embezzlement than usual. Nowhere was this direct influence more visible than his involvement in financial state matters. (Jones, 1992, p. 79). In doing so he stepped on a lot of toes and this approach to governing was generally hated by the social elite who felt their power and authority infringed on. It was part of this animosity that would lead to Domitian's bad relations with the senate, eventually leading to his death, and ultimately to an undeserved damnatio memoriae through which he was vilified by his successor and the senatorial elite who had hated him. This was of course not the sole reason for this conclusion to his life, but certainly a contributing factor. As such it may explain in part why other emperors did not engage in such practices as often as you'd expect.

Southern 1997, Domitian: Tragic Tyrant
Jones, 1992, Domitian

I'm not entirely sure that we can peg Domitian as the only Roman emperor to take these sort of steps. Yes, Domitian's actions were relatively dramatic compared to the measures used by his predecessors and successors, but it isn't as though the knowledge of inflation was lost -- it's just that it wasn't necessarily viewed as "inflation," per se. The later emperors certainly did have an understanding that faith in the public coinage was extremely important, and they did understand that rapidly rising prices had a deleterious effect on social stability and government control.

For example, we can clearly see later cases where Roman emperors -- even during the extremely volatile Third Century Crisis -- directly intervened within the monetary system of the empire in order to restore (rather than debase) the coinage. And these actions even occurred at times when they might come at a meaningful cost to the administration. Aurelian, who ruled from 270 to 275 CE, once faced a localized currency crisis based on fraudulent coinage debasement, and he actively "restored the public credit, by delivering out good money in exchange for the bad, which the people were commanded to bring into the treasury." (Gibbon's phrasing in Chapter 11 of Decline & Fall, based primarily on Eutropius and Aurelius Victor, as well as being mentioned in the Historia Augusta). So, as we might expect, the emperors never stopped understanding that public faith in legitimate coinage was well-worth effort and expense.

Aurelian went even further than the simple re-issuance of bad coins, however, and attempted a systemic overhaul of the coinage system. He altered the precious metal content of the various denominations, re-issued coins with new values or compositions entirely, and generally strove to improve the solidity of the Roman monetary system. Which isn't to say that this worked, or that it overrode the other problematic factors at play, but it certainly emphasizes that the emperors did not lose their understanding of such issues. Aurelian would not have (almost) doubled the silver content of certain coins unless he had some inkling of how important a stable, trustworthy currency was.

Beyond this, we also see cases where -- at a more macroeconomic level -- emperors realized that rapidly rising prices were deeply problematic for the empire as a whole. In 301 AD, Diocletian issued his well-known 'Edict on the Sale Price of Goods' (Edictum de Pretiis Rerum Venalium'), often called the 'Edict on Maximum Prices.' It was famously ineffective at actually taming prices, but it is evidence that attention continued to be paid to these issues. The document (which is not extant in its entirety, sadly) covers everything from coinage values to the penalties for speculation, and most notably attempts to cap prices for specific, individual goods at a pre-defined level (well, levels, really, since there were hundreds upon hundreds of items listed). There's an English translation of the edict here, if you'd like to see the variety of products involved.

None of this is to say that the emperors had a rigorous economic understanding of how monetary policy worked, but we can certainly maintain that even into the later Roman empire -- and even in the face of rather challenging situations -- the administration continued to have an internal conception of price-levels, coinage stability, and the monetary faith that public did (or didn't) place in the denarius. Other, more immediate factors usually prevented the emperors from succeeding in their fight against inflation -- but they were certainly still engaged in the monetary struggle.

I have commented on currency debasement in the past and I hope this might help you.
Filippo Schiassi in 1811 confirmed that Augustus’s denarii (98% pure) were as pure as Republican ones (excluding the debased legionary denarii of Marcus Antonius). The Republican and Augustan denarii therefore represented Roman coinage in its pristine state. Up to the reign of Claudius the denarius had maintained its Republican weight and fineness and had full intrinsic value.

Debasement of the Denarius under different Emperors

For two centuries the Roman Empire successfully operated a bimetallic currency, the denarius and the aureus with the ratio being 25:1. About 64 AD Nero slightly debased the denarius, raising the percentage of base metal to about 10% and reduced the weight of both coins. He thus maintained approximately the same ratio between them, and the 25:1 relation remained unchanged. Trajan again slightly debased the denarius, reducing its silver content from 90% to 85%, but this change did not upset the 25:1 relation; the fact that the same emperor put large quantities of gold, the captured hoard of the Dacian kingdom, into circulation, no doubt slightly lowered the price of gold and thus counteracted the debasement of the denarius.

It is clear that the denarius was regarded as the standard coin. Accounts, public and private, were kept in denarii or in sesterces, which, though no longer issued in silver, remained a unit of account. Most transactions of ordinary life must have been conducted in the denarius and its bronze and copper subdivisions, since the aureus was too valuable a coin to come much into daily use.

It was only the denarius that was debased. In Marcus's reign the silver content of the denarius sank to 75%, in Severus's to 50%. Caracalla issued a new coin, about 3/2 times the size of the denarius, called the Antoninianus. Meanwhile, the aureus was still issued at its original purity and weight until Caracalla, who slightly reduced it. The reason for this curious inconsistency was probably that the great mass of the expenditure, notably the pay of the troops, had to be made in denarii, whereas there was no pressing reason to debase the aureus.
Cassius Dio, writing late in Severus's or early in Caracalla's reign, still speaks of the aureus as worth 25 denarii. The emperors may have hoped, at first at any rate, that the debasement of the denarius would pass unnoticed, or may have thought to maintain its value by keeping it at 25 to a still un-debased aureus. This can only have been an official rate. The number of denarii circulating in the Empire must have increased considerably as a result of the successive debasements, and prices, including that of gold, must have increased substantially. Although custom would have maintained the 25:1 ratio for a while, it is hardly credible that by Dio's time there was not a black market in aurei.

Even as an official rate, the 25:1 ratio may have had little meaning. For the government would not, except in such special cases as that mentioned above, pay out good gold when it could pay in bad silver; and indeed Dio complains that Caracalla used his gold to pay subsidies to barbarians (who, as hoards prove, refused the debased denarius and Antoninianus) and fobbed off his subjects with debased silver. On the other hand, no citizen would pay his taxes in aurei, when he could pay them in bad silver. The government could only obtain gold through the levy of aurum coronarium. This was a nominally free will offering, originally of gold crowns, but by this date of bullion, made to the emperor by the cities of the Empire on such auspicious occasions as his accession, or a triumph. Dio complains that Caracalla was continually reporting victories to serve as an excuse for a levy.
For the next fifty years the Antoninianus, which from the middle of the century completely superseded the denarius, went from bad to worse, until it contained less than 5% of silver, as well as being substantially reduced in weight. After Aurelian's coinage reform, gold issues became sporadic and rare, and were moreover minted at variable weights. It is probable that the gold coins were used only to distribute as donatives to the troops on accessions and other festive occasions, the gold being obtained through simultaneous levies of aurum coronarium. For practical purposes it would seem that gold went out of circulation, being converted into plate and jewellery. Prices as reckoned in debased denarii naturally rose.

When Valerian I was captured by the Persians in 260 BC, the purity of the Antoninianus had fallen to as low as 15%. By the time Gallienus was assassinated the Antoninianus had slid to a silver content of 5% or less – in some cases dropping to about 2.5%.

Constantine from the beginning of his reign began to issue the solidus, a gold coin struck at 72 to the pound, which was to remain unchanged for seven centuries. Valentinian and Valens even insisted that solidi collected in taxes must be melted down into bullion bars, whose weight and purity could be readily checked, before trans- mission to the treasury. One of the factors which kept the solidus up to standard was no doubt the constant re-minting which this procedure entailed.

Reference
Butcher Kevin, Debasement and the decline of Rome

Jones, A. H. M*. “Inflation under the Roman Empire.” The Economic History Review, vol. 5, no. 3, [Economic History Society, Wiley], 1953, pp. 293–318, https://doi.org/10.2307/2591810.*

I have a background in economics, not history.

1. This is a tl;dr version of a much longer paper on Roman monetary history during the Crisis of the Third Century.

2. Keep in mind there is understanding inflation and then there is acting on that knowledge. We don't always do what is best for ourselves and goodness knows the Roman Empire wasn't the last time we saw rampant inflation. It's a lesson we keep having to learn.

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It's important to understand that inflation is an increase in the price level. This can be caused by a number of factors, including a change in the money supply. (More 5$ bills circulating, the value of each 5$ decreases.) Small, steady amounts of inflation is generally a good thing as it means your economy is healthy. Trade across the empire worked because coins had been standardized “by decree of Caesar Augustus in 15 B.C.E.” (Pense 213) and the coins were trusted.

So why was the economy such a mess during the Crisis of the Third Century? The emperors were busy focusing on other things.

Over the years, emperors were reducing the percentage of silver in each denarius to increase the volume of coins they were capable of minting because the increase in the money supply allowed them to finance their military goals. By 194 CE, Emperor Septimius Severus (193-211 CE) had debased the coins to less than fifty percent silver (Le Glay 424). The coins were no longer trusted.

There were 26 legitimate emperors during the third century — all of whom came to power by military coup, and only one of whom died of natural causes (Peden). This instability meant that the political climate was in a constant flux; emperors chose to concentrate on buying the loyalty of the military in order to stay in power rather than stabilizing the economy. In his final words to his sons, Emperor Septimius Severus (193-211 CE) said “enrich the troops; ignore everyone else” (Peden). And that's what they did.

Gold coins had started at forty-five coins to a pound of gold under Emperor Augustus (29-14 CE) and risen to seventy-two coins to a pound during the crisis. Diocletian (284-305 CE) managed to raise the weight of coins to sixty coins to a pound of gold (Peden). Diocletian tried to reestablish the integrity of Rome’s monetary system by introducing new monetary reform, but the situation was real bad. Despite his efforts, the Roman economy remained in shambles.

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References

Le Glay, Marcel, Jean-Louis Voisin, and Yann Le Bohec. "A History of Rome."

Peden, Joseph R. "Inflation and the Fall of the Roman Empire." <https:// mises.org/library/inflation-and-fall-roman-empire>.

Pense, Alan W. "The Decline and Fall of the Roman Denarius." <https:// www.lehigh.edu/~inarcmet/papers/pense%201992.pdf>.