Identities and accounts are two separate matters.

Accounts can only be some of identity's credentials. You are not your email address (and you should never be considered so), but your email provider can optionally act as one of trusted third parties who can assert your identity. Not the other round.

Also, you can't really own a domain name — you can only rent it from your domain registrar, in almost a same manner you rent your email account. And the idea of paying for keeping my own identity somehow frightens me.

> Which is why everyone should have their own domain name

Better never let it expire, though

The problem is that by all measures, Google is the most reputable provider... of course there are some problematic stories from time to time, but they probably happen also with paid providers, just that you don't hear from them so often because there are less people using paid providers! :)