To clarify the question, I'm not asking for an exhaustive list of what the Romans did well. Rather, I'm asking what was so unique about their circumstances that no other complete Mediterranean empire ever arose, and how after the Romans very few even managed to united Italy for at least another thousand years, much less the rest of their core domains.
More specifically, for many major, ancient long lasting Empires, there is a repeating patterns of their geographical heartlands and limits. For example, the Chinese heartland has unified, fragmented and unified again numerous times. The Persian Empires almost always contain the same heartlands as their predecessors. Most of the Northern Indian empires throughout history occupy the heartland. Same with Egypt, the Anatolian states, or even the entirety of the Eastern Mediterranean.
To be concise, it seems many of these regions repeatedly come under the same regimes and empires throughout history. There almost seems like geographical and ethnic fate for the core regions of these empires to never be splintered for long. One can say it's logical for these great empires to arise again and again out of the same place, and occupy roughly the same core areas.
Obviously there have existed many empires who go far beyond these traditional borders (that is to say, empires that combined large swaths of previously unrelated territories), and afterwards we never again see those territories under the same authorities. But it seems most of such empires never last very long, and they quickly dissolve back to the status quo.
For example, Alexander quickly conquered and combined Macedonia, Greece and the Persian empire. Yet just as quickly the empire dissolved back into pieces that fit pretty neatly with predecessor states and empire (i.e. it dissolves roughly into the old territories of Egypt, Median Empire, Hittite Empire, Greece).
Same with the Mongols. As quickly as they conquered, they dissolved even quicker into 4 pieces, 3 of which geographically correspond well with older empires (Persia, Qara Khitai, China). Even the Caliphate dissolved similarly within time.
But the Romans seem special. They completely dominated the Mediterranean for what, 500 years? Much longer than most of the "one-and-done" Empires in history. For centuries the Romans held off the decay into their original constituent states, seemingly without extreme difficulty. Yet afterwards barely anybody managed to unite Italy, much less the Mediterranean.
Justinian came close to ruling the entire Mediterranean, yet that effort exhausted the Byzantines, so much so that in hindsight we consider the reconquest to be a hopeless venture that could never have lasted, despite massive military victories. Why was it so incredibly difficult, and almost logistically impossible for the Byzantines to fully recreate the Roman empire? And for that matter, virtually anybody else?
Was it simply because the Romans were fortunate enough to greatly develop in technology and organization at a time when none of their neighbors could match it? And once the people of the Mediterranean semi-reached parity with each other, it became impossible for any one of them to dominate all of the others?
Or were the Romans of the late Republic/early Empire just... special?
TLDR; why is it considered pretty much impossible, in the post-Roman world, for anybody to recreate the borders of that empire in a lasting manner? What changed in those centuries of Roman rule, that turned the reality of a lasting, united Mediterranean into a pipe dream?
This is a question that has been around since the days of Rome's expansion: the historian Polybius actually wrote his book to explain to contemporaries how it was possible that Rome, emerging from the comparatively marginal western Mediterranean, was able to become masters of the area in such a short amount of time. His focus was primarily internal: he believed that the Roman political system had more or less hit the "sweet spot" in terms of its organization, in that it was dynamic enough to change to new circumstances but stable enough to not collapse in on itself. The army also got credit, as the Roman war machine was regarded, correctly, as a step above all its opponents. There has been a lot of nuance, debate and reworking of this argument but the basics have remained more or less relevant two thousand years on.
Instead, I want to focus on the external situation, because Rome was actually very lucky in quite a few ways. For one, it never really faced two major enemies at the same time. If, for example, the Gallic kings of Italy had risen ten years after they had they would have been fighting along a renewed Carthage under Hannibal and perhaps would not have faced a rather ignominious defeat at Telamon. When the threats were a bit closer to each other things went poorly, such as when Mithridates attacked just after the a major civil war and very nearly caused the entire eastern empire to collapse. And of course in the third century CE when Persian and German expansions coincided the empire came very close to collapsing. So blind luck played a role.
Alongside this, though, the political situation in the Mediterranean was favorable for something like Rome. Its expansion was somewhat video game like, in that it didn't face outsized threats after the fourth century or so. The Rome that faced Pyrrhus probably could not have defeated Carthage, but within a century it had absorbed its conquests and added them to its strength. This was because Italy was just marginal enough that it didn't attract the notice of the wealthier powers in the East, but it also wasn't some sort of backwater. Unlike Sicily, for example, which was the battleground of empires for centuries. And as for its opponents in the East when it did face them, they were the right mix of being state societies, so that Rome was able to simply co-opt the systems it conquered, while also not being super well governed. They were never able to levy their superior economic potential into military potential, and they were also always fighting among themselves.
For why nobody did it before, probably in part because Rome was the first empire to think of the Med as "Mare Nostrum".
This is both a answer to your question and not.
If you asked a roman your question he would certainly say: "That's easy, we were meant to conquer everything. It was our destiny". This idea is probably best represented in Virgil's "Aeneid", notably in the following passage:
Others will cast more tenderly in bronze / Their breathing figures, I can well believe, / And bring more lifelike portraits out of marble; Argue more eloquently, use the pointer / To trace the paths of heaven accurately / And accurately foretell the rising stars. / Roman, remember by your strength to rule / Earth’s peoples—for your arts are to be these: / To pacify, impose the rule of law, / To spare the conquered, battle down the proud.
Virgil lived in the end of the first century BC and was a contemporary to Augustus, Rome's first emperor. So this was written in a moment where Rome's rule was reaching its height, but the idea is probably older.
It was certainly widespread among Rome's elite and was present in the mindset of romans for a long time. This is an account by Peter the Patrician (c. 500-64) about the peace talks between the Romans and the Persians after Galerius had utterly crushed the Persian armies and was raoming free in their heartlands:
For you guarded the rule of victory well in Valerian’s case, when you deceived him with tricks, took him captive and did not release him until old age and his shameful death, when you, after his death, conserved his skin with some disgusting method and thereby afflicted the mortal body with immortal offence.’The emperor went through all this and added that his mind was not changed by what the Persian embassy tried to convey, namely that he should respect human fate (because one should rather be enraged by this if one considered what the Persians had done), but that he would follow the footsteps of his own ancestors, whose custom it had been to spare their subjects but to fight the ones who opposed them;
The reference to "Aeneid" is very clear in the last sentence.
Of course, this is more of a justification than a cause. And I doubt any serious historian would argue the romans conquests was divine will. But it's interesting to note that the romans did have an answer to your question (at least the why it rose part). And without a doubt that kind of mindset helped the Roman Empire achieve its success.
This is, of course, a classic question in Roman historiography. How did one tiny village founded on a hill in Latium come to hold sway over the entire Mediterranean? Polybios posits that is was Rome's "πολιτεία" or constitution, for more information see Polybios book vi. Mommsen, the great German historian, believed that Rome conquered the Mediterranean in self-defense. Indeed, this is greatly similar to how Rome's own historians defended Rome's actions, even Polybios mentions φόβος or fear's role in Rome's conquests. A watershed monograph in the study of Roman imperialism is W.V. Harris' "Roman Imperialism," in which he propounds that Rome was spurred on to conquer the Mediterranean on account of self-enrichment and cultural/social reasons. To expand on the former: the Romans wanted to conquer because they liked wealth that came from conquest; to expand on the latter: military success was integral to a Roman elite's standing in society and, in many ways, dictated his success in the politics, one here recalls Sallust's certamen gloriae. For example, most praetores triumphales reached the consulship prior to the first century BCE (if I recall correctly the number is something to the tune of 19 out of 21). The study of roman imperialism had entered a sort of fallow period, but economic imperialism has become more or less accepted. If this really interests you, you should consider reading Harris' monograph, though be warned: none of the ancient texts are translated.
One factor appears to have been the systematic militarization of Roman society coupled with a process of replacing small farmers with slave labor.
I was taught the process was something like this:
It was a self perpetuating cycle that allowed a significant % of men to serve and that drive intense pressures to keep expanding.
Significant food imports also freed manpower for service.
I think there are some flaws, but Arthur Eckstein wrote a book called Mediterranean Anarchy, Interstate War, and the Rise of Rome. His central thesis was the Roman flexibility and ability to incorporate their conquered enemies into their system of government (usually not entirely, but with gradually increasing privileges) and their ability to harness their manpower in future conquests went a long way. The book is written from a political science perspective and, imo, convincingly argues that the normal state of being at the time was war (everyone was either at war or planning for a war) and international law was at a minimum.
I think the most illustrative example is the Second Punic War. During that war, the Greek cities rebelled, but the Latin cities never did and Rome was able to harness their manpower to the point that, even after Cannae, they were able to field enough Legions to harass Hannibal and to conquer Spain (and support efforts in Illyria). But I certainly wouldn't go so far as to say it was preordained. The Seleucids had just a strong claim to lasting empire in spite of their serious flaws. Eckstein was able to demonstrate the balance of power in the Diodichi and, when Antiochus started to upset that balance, Rome was invited in. Romes success created a new status quo where she was able to dominate the entire Mediterranean.