Most profile fields can already be specified during the SSO process which is super-useful. From username to name, to bio, and even website was added last year. But, there’s some still minor quirks:
locationseems to be missing — from a cursory look, seems to be the only obvious field that isn’t possible to change using SSO.
websitecan be specified during SSO, but unlike most (all?) other SSO profile fields, it doesn’t have a corresponding site setting to allow overriding the local value and prevent user from changing it.
I’m guessing these were just overlooked as the code base grew over time, as I can’t think of a reason for these exceptions. Unfortunately my Ruby and Discourse knowledge isn’t enough to submit a PR, but I wanted to report it — perhaps someone has the technical chops to do it.