> I paid for it, so technically, don't I own it?
There's a lot of scenarios where you wouldn't want purchase of service to transfer ownership. People providing services have rights too. You don't get to do whatever you want with their brand, trademark, copyright. And you don't get to expect more service than is promised, or that you won't have your service taken away if the service owner doesn't want to deal with you anymore.
So you ask, well how can I be protected as a user of services? And the answer is: competition, being an informed consumer, and the occasional regulation.
> Do we own our identities? Do we own our phone numbers, emails, handles, PO boxes, addresses?
Those are all great examples of why there is no simple answer.
You do not own your phone number, but you do have the right to transfer it between carriers, thanks to regulation. You don't own your own email address, but you can rent a domain name and do what you want with your email address while you're renting the domain. You don't own your handle unless it is your real name and you go to court to protect it. You don't own a PO box, but you can rent it while you pay for it.
Ownership is often just a matter of possession. Who possesses your email address? Who possesses your PO box? Hell, who possesses your house? The land it's on? The access people have to it? The impact it has on neighbors?
Identity and ownership are complex ideas that are involved in many different levels of our society. As much as people want it to be simple, it just isn't. And the world is not going to get less complicated.