Originally websites had usernames and passwords. Username was used as a primary key (such as this website).
Using the email address directly as the username/key is a more modern trend (mid-late 00s). I believe this coincided with the dominance of gmail where people would have a forever email address. Before that, your email address would regularly change if you moved ISPs/schools/jobs so it wasn't a good identifier.
Recently i found that several services I “signed into with Google” allow neither converting to a password nor binding to a different Google account. B2b SaaS apps in fact.
