Apple would have to provide its own internal standard for screens, and show that the replacement screen did not meet the standard. Replacement screen manufacturers now potentially have access to the Apple standard, and can build parts that meet it.

They could just buy a bunch of products, replace some original parts with their own aftermarket or repair parts, then wait for something else to break under warranty.

If the manufacturer denies warranty coverage from the replacement part, the proof can be used to improve the product. If the manufacturer doesn't deny coverage, that's evidence it is an acceptable, non-interfering replacement.