After Marathon they seemed to begin getting the idea that Hoplites were a very powerful weapon that could defeat their normal light-armored troops. Instead of constantly hiring unreliable Greek mercenaries, why did they not just produce their own heavy bronze armor and train their own soldiers in Hoplite tactics? Surely the empire had the time and resources to do something like this. If Alexander could do just this just after his return from India, why didn't they?
I don't think we have any evidence to show why they didn't do something, but it seems reasonalbe to assume that as the conditions that rose to hoplite fighitng in Greece did not exist in Persia they never naturally gravitated towards it. And while the Persians certainly could have equipped and fielded a large hoplite army it would've been very expensive to do so. Training them without any hoplite experience of their own could also be difficult. They had a tried and true method of using light infantry and cavalry to outflank and surround their opponents with numbers.
Also using heavy armor on in the Middle East would've been very hot and very exhausting, even just carrying it. The army would move slower (and thereby consume more resources before the end of the campaign).
tldr- I think their lack of familiarity with the fighting style and the high cost of implementing a foreign system was enough to make the Persians stick to what had won them their empire.
First off, it's important to note that "hoplites" span some 400 or 500 years and 1000 poleis from Spain to Turkey, so we should keep in mind that there were many developments over that span of space and time. Body armour was not always worn (and in any case could not always be afforded by everyone), helmets changed styles, and more and more mercenaries sold their services to other Greek states as well as Persians and Egyptians, so it's important to be aware of over-generalizing.
My own personal opinion on this is that it is important to understand Hoplites not as a technological phenomenon, but as a social one.
It's not that the large shields, helmets, long spears and dense formations were not important, but that just hanging an aspis on some Persian dude does not a hoplite make.
A critical element of the success of hoplite armies against the Persians was the cohesion of the units, both between the rank-and-file men and between the men and their commanders. Because a hoplite in most cases had to buy his own kit, he would have been a free and prosperous member of the polis with a very strong vested interest in the success of the state. In places like Athens, he would have had even more participation in the state's power structure through voting on important decisions and participating in juries and ostracisms and so on - but even in poleis that were oligarchies or tyrannies, even a strong ruler(s) had to consider the interests of a well-off class of free citizens who were armed and organized.
I'm not well-versed enough in the social structure of Achaemenid Persia, also a very heterogeneous phenomenon, to speculate as to whether it had enough of an urban, prosperous and independent population with at least some participation in the power structure of the state to have made the development of a hoplite-style social class even conceivable. Bear in mind also that there was never actually such a group as 'Greek Hoplites': there were Athenian Hoplites, Spartan Hoplites, Corinthian Hoplites and so on - each group would have had intense local loyalties, but despite the best efforts of people like Isocrates to get other Greeks to identify Athens' interests as being those of all Greeks, not many people seemed to have bought his spiel. My point is that the Achaemenids ruled such a large and diverse area that the thought of developing a social class willing to pay for the honour of dying for "The Empire" is hard to fathom, and even less that the Achaemenid kings would have been willing to consider sharing power with commoners on that scale.
I've glossed over quite a lot, but in a nutshell, the Persian empires didn't develop hoplites on their own because they lacked the necessary social structures to develop them. Wealth and political participation are key elements, as well as an granulated urbanized environment that allowed for continuous conflict between small states that fostered competition and innovation.
Anyways, these books would be a good place to start:
Robin Waterfield: Xenophon's Retreat Hans van Wees: Greek Warfare, Myths and Realities J.E. Lendon: Soldiers and Ghosts