No. You just cant password reset if you lose access to email. You can still log in.

The email is ultimately the second factor that lets you make important changes to the account in many cases. For example, changing your password. It's more important than the password in nearly every security critical account I have.

This is not always the case. Reddit sometimes locks the account until you verify it or reset the password by email. Happened with my email pointed at a .tk domain and I had to call freenom a bunch to get the domain back.