There's a way to do auth with just email as well. Any good service will have a "I forgot my password" flow. Instead of using passwords, why not use tokens you email them gated by a 2FA challenge?

I have both Google and Github Oauth flows added to this idea in code, and it works great for my purposes. Prior to coding agents, I wrote the code by hand and went over it a few times to ensure it worked and was safe (for the email token thing at least). I even wired up the Oauth stuff myself, without an agent. It's not hard.

With agents, it's super easy to audit this and also deploy services using them, so I'm not sure why any arguments here mention how hard it is nowadays. It's not hard, but it does expose what site a user is logging into. That's just a easy function for the user though, with known risks.

With Google email, if I use a site with email logins, Google STILL knows I used them. It's just in my email instead of a logfile that I authenticated to a site. I would note that as long as the token is alive, dependent on the provider's choices, Google doesn't know I'm going back again, and has no idea what I'm doing on the site. I'd trust Google over anyone else about this, even Github (as related to Oauth to avoid the nitpick that has been common here recently).

I would hardly call this a "security nightmare" (as someone else said, not you) as Google only knows someone is authenticating to a given URL which they've vetted (a little) during the setup process. Same for Github. If you don't like Oauth, or feel that then every site someone uses should provide an email login fallback.