I don't use my phone to log in to anything. All my stuff is done on a computer with a password manager. At no time am I even likely to rely on Google for anything this important; every other week there's a thread about Google killing off accounts for no reason. No way would any sane person allow Google access to this with their track record. And this isn't even considering my suspicion that Google only wants to "help…
I’m with you, I de-Googled all my services a few years ago, and I couldn’t be happier with the decision. I’m curious though, what’s preventing you from using a password manager on your phone? I use KeePass, and I’m able to use my password DB on any device I want.
Also are you worried about the security of the DB on your phone? My password DB's passphrase is a good 50+ characters long, which I can type quickly on my laptop, but I can't imagine pecking that out on a phone. And I feel like I would not want the DB unencrypted/unlocked all the time on my phone; given the possibility of my losing it or it getting stolen, I'd want it to re-lock immediately after each use.