I'd say it's way more obvious than using a 3rd party email service.

And that's another thing: if you use a 3rd party e-mail service then you have to trust a 3rd party not to abuse that. If they have control of that email address they can take over your account. If it's a temporary address, who's to say when that address gets reused?

If you don't use a 3rd party service then you have to have your own domain for that e-mail address, that domain name can then also be traced back to you.

If you want it to be anonymous, you shouldn't use e-mail at all and only allow passkeys.