I quite agree with your post, but :
Even if Gaulish and Latin were similar, Caesar required interpreters to understang the Gauls or to be understood from them, which tends to mean it was not so easy to pass from a language to the other one.
to go further on latin and celtic gaulish connections, they are not very tighter than their connectiosn with proto-germanic languages, quickly said : western I-E languages - but by no mean was it possible for an italic speaker (a lot of difficulties of understanding between latin and osco-ombrien languages yet!) to undertstand a celtic speaker, maybe already 800 years B.C., and sure at the Julius Caesar time !!! in place or searching the few understandable words of common origin, we have to search the everyday life needed words an compare: no way to go very farwitjout aninterprete -
big problems: loss of common words + I-E 'P' fall in celtic + lenition in celtic + 'Kw' >> 'P' in gaulish and brythonic + I-E *BH >> B in celtic+germanic but >> F in latin and so on and so on...
latin was adopted by the big majority of the countries conquered by Rome thank to the system of social promotion instaured by the Empire for the vanquished elites (to become roman citizen) and the military and commercial net - South Germany, Belgia, lot of Britannia, of Iberia, Romania, Norica, and other lands that lost the latin for the great historic invasions, all of this countries was almost entirely latinized: it's not by force but by organization and time maybe 400 for Gaul - celtic languages was spoken in Switzerland and Bohemia after that yet, according to some scholars, and perhasp in western Aremorica ... the lands that keeped their language was the most remote ones, outside the core of the big commercial traffic.