> most of the time "AI" means "your stuff is going to our servers".

It almost always does but only because it is offered this way, it is not a hard technical requirement. There is nothing that would prevent offering a standalone version running locally for customers with their hardware powerful enough.

Most everyone I know in real life do not care about that kind of privacy. They happily upload anything to anywhere on the internet. The people who do care tend to fall in one of two categories: More tech inclined (programmers), or the same kind of person who doesn't use online banking because they are afraid of losing their money.