The Romans were assimilating the goths quite well right up until the end. When Flavius Odoacer deposed Romulus Augustulus in 476 with the backing of the Senate in Rome and the former western emperor Julius Nepos. When Nepos was assassinated in 480 Odoacer led a army into Dalmatia to pacify the province and punish his murderers.
Odoacer recognized The Eastern Emperor's more senior authority and in return Emperor Zeno granted the Western Empire to Odoacer to rule in his stead as King of Italy and Dux of the army (Dux is the origin of the noble title of Duke.) Odoacer kept in place roman law the west kept on running like it had for the last few hundred years. When Zeno inticed Theodoric the great to depose odoacer he ruled in much the same way. Theodoric actually spurred a new roman golden age in italy and built many great works like the old emperors had.
The point is the only difference between Odoacer and Theodoric and any of the dozens of usurper emperors in Roman history is that they did not take the imperial title for themselves. by recognizing the Eastern empire as the more senior power they were able to cement their rule. They ruled in the East's name, They took their Authority (ceremoniously) from the East and saw themselves as citizens of the empire.
The Roman state continued on in most respects, just without a Emperor in rome itself. until Justinian's gothic war in the 6th century absolutely devastated Italy, ending antiquity in the west and beginning the dark ages.
it was this massive power vacuum after the collapse of all central authority in western europe because of Justinians foolishness that led to the Bishop of rome usurping much of the power of Roman emperorship to himself. The church absorbed much of the surviving bureaucracy in the west.
but even after all that most every government in western europe strove to emulate roman power. they copied roman laws, took roman titles and even the most simple of governmental actions - the minting of coins was roman in form (and actually caused many political scandals as the emperor in constantinople claimed sole authority to mint coins in all of europe).
It's true that most of the Germanic peoples who settled in Roman territory did take a liking to things like the more sophisticated Roman legal codes and infrastructure, however full assimilation into (the shell of)
Romanitas did not quite happen until they converted to Roman Christianity (as opposed to the Arian heresy, which became heavily associated with the Germanic barbarians once it fell out of favor with the actual Roman emperors for good between Constantius II and Theodosius I) and became largely indistinguishable in language & customs from their new Romance-speaking subjects/neighbors. For the Visigoths, that happened in 589. Before Reccared's conversion that year, the Visigoths largely lived separately from the Hispano-Romans who constituted the majority of Iberia's population, still mostly spoke Gothic (as it was the language the Arian Bible had been translated into by Wulfila), and abided by a separate Gothic code of laws - the Code of Euric - which could get pretty severe in places, like outlawing Roman-Gothic marriages (a ban lifted by Reccared's father Leovigild, who moderated the Gothic/Hispano-Roman segregation without abandoning Arianism himself). (Also, a minor quibble but Odoacer wasn't a Goth, he was Scirian and his dad Edeko actually got killed by the Ostrogoths in an earlier battle for control over Pannonia.)
As you say, the Ostrogoths never got the chance, which I think is a pity because Theodoric was indeed more forward-thinking and Latin-friendly than his cousins among the early Visigoth kings. The Gothic War was absolutely ruinous for Italy, and all just for a pathetically short grasp by the ERE on the peninsula before the Lombards strolled in and took it over anyway. The mind boggles at what could've been had either the war not happened at all (probably by way of either Theodoric's grandson Athalaric not dying young or his mother, Theodoric's pro-Roman daughter Amalasuintha, not getting deposed by her jackass cousin Theodahad) or Belisarius gotten enough of a dent in his famous integrity to accept the Ostrogoths' offer to claim the vacant Western Roman imperial throne for himself. A strong Italy would've been hugely helpful in combating the rise of Islam less than a century later, which to my understanding was the main reason for the collapse of the Romans' Mediterranean trade network (which was what really 'darkened' Dark Age Europe by severing the smoothest way of communicating & trading between the pieces of the former WRE, even accelerating the fragmentation of the Romance languages). A Belisarian Italy might've been able to even save North Africa.
Speaking of North Africa, a people who did assimilate more smoothly into
Romanitas compared to even the Goths would've been the Mauri/Berbers and former Punics of Carthage, since they didn't have a religious barrier to integration and also had a much longer history of being Roman vassals (going back to the Numidians).
Even had their own distinct Vulgar Latin dialect turned Romance language which was apparently close to Sardinian and lasted until the high/late medieval period. They actually did almost go their own way too, lifting up Heraclius' kinsman Gregory as a challenger for the purple after the Emperor Constans II (Heraclius' grandson) pushed the Monothelite heresy, but unfortunately it had to happen right as the Arabs were caving the Romans' shit in from Syria to the Maghreb,
to disastrous consequences. Again the mind boggles at what could've been, imagine how history would've unfolded with a strong Catholic kingdom based out of the former Western Empire's breadbasket, keeping the Maghreb greener (agriculture in that area wasn't totally destroyed until
the niggers of the Banu Hilal tribe arrived in the 11th-12th centuries) and the Muslims well out of Spain, projecting Christianity & Roman civilization into West Africa, etc...
