Genuine question, what would you write instead of "proceeded to"? To me, as a non native English speaker, it seems reasonable to use this expression, and it would not even stick out to me tbh
"Went" is a powerful word. With suitable helpers it can replace "proceeded", as you demonstrated, "attended" ("I went to a good school") as well as "became" ("On hearing this, Joe went all silent") or "said" ("So then she went 'Dude!' and we all laughed") and hundreds of other words.
Only a handful of words ("got", "y'know" and "fuck") rival its versatility.
I didn't claim that this was exclusively American. Though I'd have to admit that one doesn't have to be American to adopt Ameracanisms: rhotic Rs, Netflix color-grading, and copy-cat political movements are other American cultural artifacts showing up across the world due to America's dominance of the zeitgeist.
Rap verses in pop songs wasn't a spontaneously phenomenon across the globe, the origins are tracably American - but that doesn't make all rappers American.