You keep trying to get me to do it with Chrome, so I switched from that, but now you're going to badger me about this for my phone, too?
I don't understand why it was necessary for you to switch away from Chrome. Could you be more specific? In particular, I think all your points can be addressed easily in Chrome today (and I don't think the future stuff in this paper will change that).
You don't have to sign in to Chrome. To avoid it, (checking) you have to say "Skip for now" in the initial setup of the Chrome profile and ignore the small text "Not signed into Chrome. You're missing out - sign in" at the top of new tabs. Sound right? Maybe that text is pushier than you like, but it doesn't regularly interrupt your workflow or anything. You miss out on some features like shared bookmarks between devices, the ability to see what tabs are open on other devices, and auto-signin to Google services, but it sounds like you don't trust Google enough to be able to benefit from these services.
Sometimes I want to surf anonymously.
Is there something wrong with Incognito mode? This feature has existed in Chrome from the very beginning. Of the well-known browsers, only Safari had it first.
Sometimes I don't want Site X and Site Y knowing that I'm the same person logging into both.
This shouldn't be a concern in Chrome any more than in other browsers (except perhaps if signed into Chrome and Site X and Site Y are both Google services, but that can be addressed as well - read on). I'm not aware of any major security problems in cookie handling, for example. And Chrome allows you to really easily have separate profiles for different identities. (I guess the feature's called "Users" now; it's pretty prominent in the settings.) I do this all the time - one window with a happy guy in the upper right corner for my personal stuff, one window with a ninja in the upper right corner for my work stuff. Entirely different cookies between the two windows, and they can be signed into Chrome as different Google users as well. I love this feature. I'm surprised that as far as I know other major browsers still don't have it.
And I can say for certain that all the time, I don't want to be tracked by you so you can present me with more "targeted ads" to give me a better user experience.
Okay. Then you should probably opt out of ad personalization at www.google.com/ads/preferences to stop delay of personalized ads. Set a "do-not track" cookie through your browser's preferences. (In recent Chrome releases, it's at the bottom under "Advanced Settings".) And, while you're there, if you have other Chrome data collection enabled (IIRC this was opt-in rather than opt-out during Chrome installation) and have since become concerned about it, uncheck "Use a web service to help resolve navigation errors", "Use a prediction service to help complete searches and URLs typed in the address bar", "Enable phishing and malware protection", etc. These are all things you can turn off, and it's pretty clear what you're giving up by doing so, so I think it's not hard to make an informed choice.
Full disclosure: I work for Google (not on Chrome or this paper). My opinions are my own. I have a tough time understanding these criticisms - first of all, I don't understand if you think targeted ads and the other stated reasons for this data collection are for are inherently evil somehow (I disagree) or if you think Google is secretly using them for something far more nefarious (what?). Secondly, I don't think Google makes it harder than other browser vendors / websites to turn them off. It's probably much smarter for me not to feed this discussion but, screw it, I would like to actually understand the concern. It's too vague now for me to do anything but dismiss it.