I only stay logged into Chrome to sync bookmarks/extensions, but I too strongly dislike tying the browser login to website logins. It's likely very frustrating for anyone that has multiple accounts on any Google service. Also it just doesn't feel right- those two things should always be separate actions I have to perform. My browser account is my browser account- my web accounts are my web accounts. Crossing them over is building a bridge where there shouldn't be one.

Reconsidering other browsers (and really, moving off of Google services entirely)