Well it's not that you have to be an AI to Sublime, but GP was (correctly) referring to the fact that any Mind that was created without any "training" (I forget the exact phrasing used) would invariably and immediately Sublime.
Anyway Subliming is the only aspect of The Culture series I did not enjoy. Much too handwavey for my liking. Still, made for some interesting stories.
It's been a good while since I read the books, but I do have a distinct recollection of the Culture Minds being described as being created purposely ‘flawed’ in some way (explicitly negative terminology) to prevent immediate Sublimation. I could be misremembering, though.
the culture Minds are intentionally designed with personalities (for lack of a better term) suited for their intended functions that keep them interested in/involved with base reality and their responsibilities there. there was a bit about how "perfect" Minds created without such proclivities will basically fuck off to a higher plane of existence asap. of course the culture Minds know this, they're the ones designing and building new Minds after all, and some decide that they'd like to see what's on the other side of the veil themself and that's allowed, but most are content running their ships and orbitals and whatnot
I think role of subliming was to show Culture not as pinnacle of existence but an advanced and powerful niche civilization.
In Excession main gimmick is an object (possibly unrelated to subliming) that immediately puts on alert all civilizations at Culture level of capability (and below) because it's something new in the universe, something that could help bump out of local technological minimum that the Culture currently occupies and exceed its potential in a different way than subliming, that is well known, but mostly one way road out (and very out).