In many services, email can be used to reset the password, or do something that is sensitive. Sensitive data is also quite often sent to you by email, e.g. long links that enable access to your account or similar.
However for most people, their email service provider can read all their emails, can see what is being sent, and can send email themselves as "you". So doesn't that give your email service provider basically full access to your accounts? This seems like the incorrect medium to send such information via.
I don't really know if this matters, however you never really see these email services sending you "encrypted" email with your pgp key.
Also, it is well known that email is inherently insecure, or not designed with privacy or security in mind.
However it keeps being used for these purposes.