You're right, the self-service repair program exists. It doesn't clear neither the pairing issue nor parent's hurdles though, as Apple parts are still required , you can't get any similar enough screen you'd want, and they'll be priced the same as in Apple Stores.

As far as I remember, the self-repair kits only make sense in very niche cases (I think repair shop get a different contract ?) and won't work around any limitations Apple puts on parts or repairs.