I ran into a variant of this issue: I received an email at my primary address (recovery address for Google) that someone is attempting to log into my old Google account, and that the request was blocked. I try to reset password, hoping that the reset link is sent to my recovery address but Google doesn't allow that.

The only option is to "try and enter the last password I remember". Besides that there's no way to reset the password.

Why even bother informing me at my recovery address about the suspicious login then?

As long as a recovery address exists, it must be able to reset password?