Sure. Everybody can.

But Google Analytics is a 30 second setup, whereas setting up a log analyzer (or even getting logging going in the first place) is a much bigger hassle. Some of my stuff is on wacky Cloud Function hosting that I wouldn't have the first idea of how to go about logging.

Thus, nearly 100% of us just use Analytics. If they had an "evil" checkbox that I could uncheck to stop it doing whatever you're worried it will do, then I'd happily do so.

Frankly, I'm not sure what GA could do that would bother anybody. All it does is tell me how many people saw what page and how long they stayed there. It certainly can't tell me anything about you personally.