Why did they always have to tie their civilization to the Romans and not be able to start their own empires without paying lip service to how they were a caesar of some kind and the nth Rome
It's certainly an interesting question, and our modern conceptions of the state probably do a lot more harm than good when it comes to thinking about the political ideas/realities of ancient or medieval peoples. Especially so when it comes to the type of binary political decisions that are used in a video game like Crusader Kings II where you either "create de jure empire" and resurrect something that already ostensibly existed, or you "found a new empire" which you can customize yourself.
Personally, I think some of the explanations given in this thread are a tad reductive. It imply that it was a conscious decision to "choose" to claim the mantle of the Roman Empire as a pragmatic form of realpolitik to gain political clout and/or legitimacy. This naturally leads you to ask "Why?" Why didn't they just choose to base their legitimacy on something different, like the older Germanic traditions of the Franks. I would say that this wasn't really an option for a number of reasons. First off, much of Western Europe had experienced
centuries of Roman rule and/or contact. The time of Caesar Augustus to the "official" end of the Western Roman Empire was a span of nearly five hundred years. That's about twenty generations of imperial rule. If you were living at the time we deem the end of the Western Roman Empire and if every man in your direct paternal line lived an average of 45 years, then your
great-great-great-great-great-great-great-great grandfather could have been living in Imperial Italy around the time of Jesus' death!!
Hell, the entire concept of an empire was tied to the Roman Empire itself. Today, we know a lot about world history and have seen countless empires come and go, but to people at the time, Rome was indivisible from the concept of an empire. It colored their entire conception. One cannot exactly 'start your own empire' on entirely new foundations unrelated to Rome when Rome informs your entire perception of what an empire can and should be.
The closest comparison I can think of is if I asked you to think of a brand new political ideology in which none of its major ideas are inherited from something already existing. Next to impossible, no? Because all ideas are built on the shoulders of other ideas down back to the very first thoughts and shared knowledge. You can't really conceive of something radically new that is entirely independent of the world around you, and this was the case for medieval rulers. They lived in the aftermath of
the Empire. The people spoke languages derived from Latin or influenced by it, they practiced a religion intrinsically tied to the Roman legacy, and their political practices (think Carolingian 'feudalism') were directly the result of the collapse of the Western Roman political system. So, it would seem that to break free from the legacy of Rome and step outside its shadow was essentially undoable because they lived in a society colored in every way by Roman history.
Even the official language of the post-Roman imperial polities, going straight on into the High Medieval Period, was Latin. One might be tempted to see the etymology of the word Reich in German and point out it’s proto-Germanic rather than Latin roots (although it comes from realm which was merely a local equivocation to
imperium rather than an organic conception of it with equal meaning), but you have to remember that the Holy Roman Empire legally wasn’t the
Heiliges Römisches Reich or the early Medieval Germanic equivalent. It was the
Imperium Sacrum Romanorum. Latin ideas weren’t only just transmitted into Germanic languages during this period, Latin instead replaced them as
the language of administration, power, and authority for these incoming peoples and I think this is significant to everything else I’ve mentioned.
You also might reasonably ask about other “organic” empires outside of the Roman context. China is an obvious one that is very similar to the Romans in their lasting power, their expression as an “idea” as well as a lasting material polity, and their culture that was able to absorb invading peoples. But for others, the situation is somewhat different. In an lot of cases, things we call an empire are sometimes just historiographical terms imposed on peoples who might not necessarily have thought of themselves in the same way that a Roman or Han Chinese might have. For instance, the Mongol peoples created what we refer to as the Mongol Empire. Yet in their own language it is
yeke Mongγol ulus or roughly the Great Mongol Nation. I’m no great expert to talk about this, but from what I understand and assume, it was a confederation of tribal peoples that incorporated tributary and subject states who paid homage to the Khan. While they had sophisticated administration and a universalist claim in common with other empires, they had a unique cultural conception of what that actually meant. It wasn’t necessarily something radically new and created from nothing, but instead a much larger and more developed form of previous steppe confederations and tributary arrangements. So essentially, it evolved organically from Mongol specific ideas and was not adhering to some universal definition of empire that exists abstractly. The same would go for any “new” medieval empire, it was born from its circumstances, which I hope to demonstrate were absolutely steeped in the Roman legacy.
To get back on track, I mentioned it in the previously, but Christianity also played a huge part in this. Christianity integrated itself directly into the fabric of the Roman Empire and, by the end, was essentially inseparable. So, of course, when the Western Roman Empire 'dissolved', the Pope in Rome and the Church was able to assume some of the former clout. They were the only institution that officially had a network all over the former empire and so it was natural that this process would occur. The Donation of Constantine, though a 9th century forgery, officially cemented this. Constantine bestowed upon the Roman Curia, "
power, and dignity of glory, vigor and imperial honor." They were given, as the story goes, imperial insignia, lands, and the right to preside over the entire Christian world (inseparable, in their eyes, from the world itself). This further bound medieval polities into the Roman legacy, by supporting the Papacy (or, with the Pope's blessing, themselves) as the successors of imperial power. Charlemagne and the Carolingian dynasty was the prime example of this process. I don't think one could reject the legacy of Rome without rejecting the Christian Church itself at this time, even in the Eastern Roman Empire. The concept of
translatio imperii is also useful in understanding this. Imperial power of Rome never 'ended' even though the polity that we retroactively identify as the Western Roman Empire fell. It was transferred from the Western Roman Empire on to new and emerging polities naturally, according to the perceptions of the time.
I'm swiping this from the Wikipedia page on
translatio imperii for the sake of brevity, but:
"
The translatio imperii idea didn't separate "divine" history from the history of "worldly power": medieval Europeans considered divine (supernatural) and material things as part of the same continuum, which was their reality."
So the divine conference of imperial power on the Papacy was not taken 'separately' from the collapse of the Empire itself. So the Pope was invested with imperial power, and could confer it as he did to Charlemagne in 800. This would maintain itself during the entirety of the medieval period.
I feel as if I'm rambling without getting my point across so I'll just say that 'an empire' and 'the Roman empire' were indivisible concepts to the people of the medieval period, and it colored the entire framework of society and their religion, and so 'breaking' with Rome was essentially impossible. They could not just formulate a new empire outside of this conception nearly as easily as we can today with our understanding of many world empires who are entirely independent of Rome. I think a comparison to China is very useful, as you yourself made earlier. I would hesitate to say people just 'claim influence from the past' as if it's a conscious process, when I think it is more useful to think of it as something that undergirded their entire social and political thoughts and realities.
Essentially, the Roman Empire was an
idea as well as a polity. I think one of the best summations comes from Crassus in Stanley Kubrick's
Spartacus (1960): "Rome is but an eternal thought in the mind of gods."
EDIT: a couple more paragraphs of thoughts against my better judgement