It's neither convenient nor stable for anyone moving between countries either. When given the choice between a service that uses my phone number as my permanent user identifier and one that uses my email, I'll always go for the latter.
Unfortunately, big parts of the industry seem to be headed the other direction.
I've been using voip.ms and it is fairly good. I wish the SMS support was a bit better but it does reliable deliver messages to email or SIP. (Large messages are not re-joined though and sending is based off of a code in the subject instead of an email address per-number which could be easily be added to an address book)
Unfortunately, big parts of the industry seem to be headed the other direction.