WTF?! If you're looking to buy an iPhone 13 and aren't a fan of AppleCare+, you'll have to be extra careful not to damage the display. If you ever need to replace it, you'll be pretty much forced to go to Apple and fork out more money than if you went to an independent repair shop, especially if you want to continue using Face ID.
Apple is well-known for its tendency to sacrifice function for form and making devices harder to repair in the process. Over the past few years, it has also become a formidable enemy of the Right to Repair movement by making life progressively harder for independent repair shops -- from trying to curb the dissemination of schematics data and diagnostic software to using various software and firmware tricks to discourage replacing certain components like batteries and Touch ID sensors with non-genuine parts.
The latter part is what iFixit calls "security through serialization" and will either disable some of the functionality on your iPhone or render it completely unusable when a third-party component is detected. With the iPhone 13 lineup, Apple seems to have taken yet another step in that direction, which is not unexpected but still rather disappointing.
As noted by YouTuber Phone Repair Guru, some components such as the ambient light sensor, the proximity sensor, and the microphone are easy to replace. Replacing the screen would also be relatively easy to do if it weren't for the following message -- "Unable to verify this phone has a genuine Apple display."
That is to say, even if you or an independent repair shop can technically do a display replacement on your iPhone 13, 13 mini, 13 Pro, or 13 Pro Max, it comes at the cost of losing Face ID functionality. Phone Repair Guru explains that, at least in theory, it would be possible to transplant some chips over to the non-genuine display to maintain Face ID, but many independent repair shops won't attempt that as it's both time-consuming and requires more sophisticated tools.
It's possible Apple may release a software update in the future to allow Face ID to work even with a non-genuine display, but don’t hold your breath. The last time the company did something similar was when it blocked Touch ID functionality, but at least in that case, it was somewhat justified as there was a security element to it. By contrast, the Face ID module is simply a capture device that doesn't hold any facial recognition data, which is stored in the iPhone's secure enclave.