Hyperbole much? You can still simply not log in to Chrome and/or Google Search. But if you want to be logged in by default, then you'll have to tell the browser when you occasionally don't, no?
Most people don't intend to log in to Google Search, as far as they're concerned they're logged in to their email account. This is why Google got in so much trouble in France and the EU over the past couple of years.
This. I don't use gmail, but I use youtube. And when you've logged into youtube, you've logged into your "Google Account". So you can't have youtube open in one tab, and not have your history from other (non-incognito) tabs logged (modulus some tweaking of various preferences that aren't obvious or intuitive).
There's no reason why they couldn't to the same thing Mozilla does: a) have a pretty clear account thing for "sync", b) have a pretty clear page for opt/in out on what to sync, c) Have working self-host sync solution, d) have an open source sync solution so you can easily see what's going on, and how things are encoded/stored.