I got myself a little confused while testing some things. The reason being that uneditable user fields are entirely hidden from non-staff users’ profile preferences. (Staff users have special privileges to edit even uneditable fields, so it shows up as an active field for them.)
I think user expectations are generally that uneditable fields are still shown, but disabled.
Unless there are any objections to this, I can make a PR. CC @chapoi.
Edit: I can imagine a reality where some moderator team are using this for “staff notes” or other secret information.
Maybe need to a) make this configurable on a per-field level, or b) add a site setting to enable it.