This has nothing to do with the phone carrier.
In the US phone numbers are much more open than any other means of identifying someone you want to contact.
"non-free" is a bizarre thing to say in this context. No identifier is going to be free as in speech - that would defeat the purpose. If you want to have assurance that you can keep the identifier it had better not be free as in beer either - the provider of the identifier could revoke it at any time.
Some sort of government-issued communications identifier might provide the needed benefits, but actually the phone number is the best solution to the problem that we have.
If you're relying on an email address, you're in much shakier territory. (Unless you own your own domain and email hosting solution, and unless you're a multinational corporation it's likely to be less reliable than other options.)