And this is a real problem because you don't really own your phone number: it's leased to you for as long as you pay for it but I don't think there is anything to prevent a telco (or VoIP service like Twilio) from taking that number back from you. This is another problem inherent in using a phone number as the source of your identity on a service. Email addresses are better but can still be subject to seizure. Perhaps the answer is what Session is doing: you get a GUID is that is assigned to you and that will never be assigned to anyone else.
Threema generates a short alphanumeric id, that is easily sharable. It will also generate QR code for you, so other people do no have to type them, just scan them.