I agree that public library access for people who don't own a computer is an important and difficult problem, but you're talking about other people, not the case being discussed now. Bringing it up here is a distraction.

For someone who is tech-savvy and owns a laptop, there is a simple solution: create a new, vanilla browser profile and use it only for logging into Google. (I do the same thing, but for Facebook.) You'd don't need any privacy extensions when you want them to know who you are.