Or another perspective: latin itself was part of larger group of languages spoken in the area, which wiped out a lot of local languages as the republic and late

Or another perspective: latin itself was part of larger group of languages spoken in the area, which wiped out a lot of local languages as the republic and later the empire expanded. Umbrian, Oscan, Picene, Etruscan. Then Ligurian, Venedic, Liburnian, Illyiric, then Gaulish, Aquitanian. The list goes on. They did live a trace in the romance languages that then spawned after latin dominance was over, but it's hard to quantify as in many (not all) of these languages shared a common ancestry with latin. The main forces that drove the creation of romance languages out of latin however do not lie in this substrate, but to a combination of natural language drift and the admixture of the languages of the new rulers and immigrants (e.g. Germanic tribes like the Franks, Longobards, Vandals, Visigoths, ...). In most cases their influence was not strong enough (or lasted enough) to fully displace the latin culture present throughout southern Europe. But had latin been left to just naturally diverge into many dialects without foreign rulers, the character of the romance languages we have today would have been likely quite difference. They could have perhaps ended up being a more similar between each other, but the lack of a unified central power and cultural attractor means they would probably have diverged anyway. Keep in mind that Latin was still used (written and spoken) as a culture language for a long time after the fall of the Roman empire. This relieved the local languages from the pressure of being mutually intelligible with people from other parts of Europe the elites, merchants, clergy etc had to interact with.