Diatopic dialects were almost unknown up to the last days of the Roman Empire, though - the state system was just too steeped in Latin to allow for reasonable differences between Roman areas. Vulgar Latin was almost completely simplified, rather than colored by substrata; as you say, the diastratic element was - by far - the most important one. Diatopic elements appeared after the fourth century in the West, and diachronic changes are... well, pretty obvious. I don't think any language can really expect to avoid them - English tries, hard, and the only end result is that spoken language is being ripped apart from written language (the Great Vowel Shift, as a linguist, makes me scream).
The Great Vowel Shift happened at a time before English was standardised - it's not a function of the ossification of the written language.
Actually - it's funny it makes you scream because it's only an issue if you obsess over the Latin sounds for letters. And if Emglish bothers you then Welsh should drive you insane, given that "Cymru" is pronounced "Kumri".
As to substata - as has been noted, there's evidence of Gallic influence in modern French and of other Italia languages in Italian cities distant from Rome - demonstrating that there was
always substrata, but likely only for the Plebs and not for the Equestian and Senatorial class, or their close servants.
This trend can be seen later throughout Europe - modern English is London English - modern French is APrisian, but whilst the ruling class and their assistants spoke these languages the lower classes spoke highly localised dialects because - unlike the Elite - they only needed to be intelligible to their local masters, not to someone on the other side of the country.
Also - we know that later, in the centralised Byzantine Empire, the spoken Greek language diverged from Koine Greek during the Middle Ages to the extent that it became difficult to understand without training.
Classical Latin was a literary construct, there's little evidence it was spoken day to day outside the Senate or the Courts. Late Latin, likewise, is an administrative language, not an organically spoken one. In both cases it's likely that these were standardised languages taught in schools and spoken by educated people, but not by the masses. Vulgar Latin is not a development of Classical Latin but of Archaic Latin.
When I worked on the Europa Barbarorum Mod for Rome Total War the mod's motto was "Quisque Barbarus est Alio". Someone complained that this was incorrect according to Classical Latin and the proper declension was "alii" and not "alio". Our language experts went back through Vulgar and archaic Latin and were able to demonstrate the "alii" only appears in Classical Latin, but it would be declined "alio" in Vulgar and archaic Latin because the Dative and Ablative are the same.
And before our mention it - yes - in "pure" Classical Latin "est" would come at the end of the phrase, but it doesn't have to.
I'm not suggesting complete eviction, of course, but it's a fact that the institutions the Lombards were seeding were truncated - in particular the institution of a solid Romano-Germanic kingdom, like it would happen in France and Spain. Quoting Montanelli:
No, the Lombards sunk into the Italians - and doubtless had a linguistic impact, on pronunciation if not vocabulary.
I, frankly, do not think there is any question that the Romans in Charlemagne's time (those people in Latium under the Pope) considered themselves in every sense "Roman" and that is part of why Leo declared Charlemagne to be "Augustus" which is the original "primary" tile of a Roman Emperor, more integral to the position even than "Imperator".
The question is how Roman were they vs how Italian and I think that the argument comes out overwhelmingly that they were still very Roman and not yet very Italian - they still spoke Latin, thought of themselves as Roman and genuine Imperial rule was within living memory for many. Hell - the Pope before Leo was every bit a Roman, born and raised within the Empire.
