I would put greater emphasis on not locking yourself out, since that's the most likely threat for many people. Losing your phone (or having it die on you) is common and you should assume you'll do it sooner or later. Print out backup codes and store them somewhere safe that you won't forget before enabling two-factor authentication that depends on you having your phone or other device that can break.
Go on vacation, loose your phone and security key (along with any written passwords) - by robbery, theft, customs or accident.
You'd still need to be able to access your email etc. or else your experience is going to be a hundred times worse.
What you really want is optional 2FA. You have a regular (unique) password but you never use it unless there is an emergency.
Now you just must make sure to remember that password that you never use, even when in distress... Not that straightforward either.
Also upon use any "smart" site would flag it for unusual activity and lock you out until you can verify it.
I guess I'm stuck with passwords.