To get Rome right it has to be a lawful evil multicultural empire that manages to incorporate representatives of all the people conquered into its elites.
What exactly do you mean here?
Because I can see two meanings, and I've heard both, and one is true, and one is a ridiculous whitewash of the other kind.
The true one (which I am guessing you mean) does not apply to
Rome itself, not to the Senate, not to the
leadership of the Western Roman Empire, but it does apply a lot as you get further and further and further from Rome, towards the edges of the empire. In those places, Rome does start having the locals be a significant part of things, local "kings" becomes rulers under the Romans, for example. Whether I'd call it genuinely "multicultural" beyond the first generation, I think is questionable, because Rome only respected or acknowledged one culture - Roman culture - it allowed other religions, but only if safely syncretized. Other cultures were barbarian nonsense to be got rid of ASAP.
(Well, and Greek and Near-Eastern cultures got some mild and inconsistent respect, but not, say, Gallic or Gothic cultures.)
Roman practiced extremely active and aggressive cultural genocide, particularly in Western Europe, and failure to acknowledge that ignores some of the very worst things Rome did. For example, there's no question that in both Gaul and Britain, the Romans did a very concerted and extremely intentional cultural genocide. Caesar writes about it, as do others like Tacitus. In Gaul you basically had 1/3rd of the population killed, 1/3rd enslaved and sent all over the empire, and the final third utterly beaten down, robbed, and forced into Roman ways, under Caesar. Caesar didn't get far with Britain, but Claudius did, and he certainly engaged in a careful cultural genocide, particularly focused on destroying the Druids and all associated elements of society. The Romans certainly thought this was pretty key. They also destroyed a lot of other elements of the way of life of the Britons, and replaced with Roman elements, which were not universally superior. For example, Roman farming techniques were drastically less efficient than those of the Britons. Yet the Romans, in their arrogance/hubris/imperial-ness (all replicated by the British Empire 1700+ years later of course) replaced them, because they assumed they knew better than these dumb barbarians.
Let's not even start on Carthage, which people still cheer about, or think was funny, which was a very literal genocide, and cultural genocide. The Romans were not, in general, interested in anyone else's culture except the Greeks, or occasionally someone in the Near East (and such flirtations were often fleeting).
The other meaning, which isn't true, but I've seen people claim, presumably because they don't really understand what's going on, is that because there was some social mobility, which like, you are being a bit silly about frankly - what you describe was the wild exception, not the rule - people start thinking stuff like that there are Goth-Romans in the way there might be German-Americans. I'm not sure you're saying this, but to be clear, that's not true. A minority of Roman Senators and similar elites were eventually of non-Roman heritage, but if you went on about it, that was a black mark on you. That was not respected. Showing significant sympathy or in some cases any sympathy with conquered peoples was not really okay, outside of the odd situation. Indeed, the only times I can think of someone getting away with it cleanly they weren't related to those people (like there were some Romans who objected to Caesar's treatment of the Gauls who were, after all, Rome's allies even as he murdered and enslaved them by the tens of thousands - but they weren't Gaul-Romans saying this).
Only in the sense the Borg assimilate.
Hell, less so because they don't really reliably add "technological distinctiveness" to their own. They tended to blithely assume their own tech is superior.
Britain and Gaul are superb examples of that. You become a cultural Roman, or you're unacceptable and have to be "dealt with". Indeed, for many Gauls, that wasn't good enough. Caesar put them to the sword or enslaved them despite them being Roman allies or "culturally Roman" in most/many regards. You really had to join the Borg collective here, and preferably become a Roman citizen. It's certainly true that many, many people, especially as I said on the outer parts of the Empire did indeed become Romans, but they had to. There's this romantic idea that people were happily signing up for the wine/baths/food etc., but whilst that was the carrot, the stick of being slaughtered, raped, enslaved was ever-presented and frequently used. Sometimes for no reason at all.
What Rome demonstrably did not do was genuinely bring cultures within the Empire unless they couldn't entirely be overpowered. Rather it deleted and replaced cultures where it could. Some it did faster and more thoroughly than others, but the goal was always full Romanization, not hybridization. On the edges of empire, that goal often failed (though I would say it perhaps did not fail in Southern Britain and Gaul), and with the Greeks it got pretty complicated, especially once Christianity got into the mix.
I'd contrast this with, for example, the Persians. The Persians did, in fact, assimilate entire cultures, and just say "Yo, whatever, we're the new boss, just like your old boss, pay your taxes here! Send us X troops when we ask!". I also think even the British Empire, much later on, tended to assimilate and cross-pollinate more than Rome did, certainly when Rome was at its height, but that is, I admit, a far more arguable contrast than the Persian Empire.
Also this is all kind of irrelevant, because it's based on the assumption that you want to do Rome "right", and frankly, why would you want to do that unless you were running a game about historical Rome?
Apologies if I'm just on a rant myself and you don't even disagree with any of this and I've just assumed you do lol! But the focus of my studies was Roman Britain and to some extent Gaul and I'm not buying any ideas about the Romans picking up local ideas or the like here (they did a little in the Near East and a lot in Greece, as noted). The Romans made a distinction, I think, between barbarians like my ancestors and smarty pants cultures they might learn from like the Greeks.
