That would be convenient, but it has disadvantages. Profile names are not unique (hundreds of people could use the profile name “John”, and their contacts could relabel them “John from work” etc., with effect just in their own clients).
E-mail adresses are unique, and if you are using a non-chatmail address, you can contact friends by e-mail address, but then your messages won’t be end-to-end-encrypted! When you share a QR code or link, you are actually swapping encryption keys behind the scenes.