In the case of parts pairing, we're not mandating compatibility with third-party parts, we're mandating compatibility with
first-party parts. Parts pairing doesn't validate that you have
a genuine part, it validates that the part in there is the one Apple says should be. The parts in an iPhone are effectively non-interchangeable, like we've gone back to 1765[0] or something.
As for third-party parts, the reason why the repair market is flooded with 80% sRGB garbo screens is because Apple took the good screens off the market. Sure, you can buy a screen assembly from their weirdly debranded parts store, but that's deliberately designed to force you to buy components you don't need. Remember, a screen assembly also means replacing the front cameras, Face ID sensors, etc. If you want to buy just the LCD or OLED and put it into an existing assembly, which is the only way any of this shit makes financial sense to repair, sorry, you're not allowed to buy just that.
The thing about manufacturer-branded repair services is that they're built like a McDonalds. Everything is designed so that they can hire the cheapest labor possible. That's why they have really expensive custom hotplates to remove iPhone glass, and why they'll charge you for a new Face ID sensor just because you need new screen glass. Component-level repair requires investing in your employees, which is the last thing Tim "Ship Jobs To 'Jaina" Cook would ever do.
The reason why people like Louis Rossmann were able to beat the Genius Bar on price was not because he was buying cheap parts. It's because he was buying genuine[1] parts produced by companies breaking their exclusivity agreements with Apple, and then investing money into his employees to do the skilled fix.
[0] https://en.wikipedia.org/wiki/Interchangeable_parts#Origins_...
[1] Genuine in the sense of "meets Apple specifications", not in the sense of "Blessed by His Holiness, the iPope".