That's not always possible.

It is almost always possible.

Email was often used as a primary key on older websites

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.

Yes, and it's possible to change that e-mail. The only place I've encountered which doesn't is Alibaba.

ChatGPT is another.

Bambu Labs online account has the same restriction for some reason as I found out the hard way, though I had thought that was extremely rare.