I mean, ok. Doesn't that just mean you aren't charging enough? Is apple charging you a percent of what you charge?
So in this example, an official Apple store offers a screen replacement for $149. Apple then announces they will sell official parts to independent shops. Apple will then offer an official screen for $135, leaving no room for the independent shop to make money unless the repair shop charges $170 (made-up number for example).
The benefit for Apple may be two-fold. Apple will go from having the most ridiculously overpriced repairs to being the cheapest for official parts. Apple may also then justify making it extremely difficult to use non-official parts (as they're already doing).
If you're optimistic, you can say Apple is doing this to make the customer experience better to help improve their stagnant phone sales. If you're cynical you can say it's a clever plot to eliminate independent repairs and force people to go to Apple stores.
I might just not understand the market here but why would I assume that my local repair shop would be able to offer me labor at a cheaper rate than Apple's huge repair system?
The issue here is that they aren't just charging the normal brand premium for the part, they're also tacking on the same premium again to account for the value of the repair service itself (even though the third party is providing that), and then a little more so that a third party repair service that wants to use Apple-branded parts would have to charge higher prices than Apple's own repair service in order to turn a profit.
The intent of the pricing isn't to maximize profits from sales to third party repair shops, it's to make them uncompetitive and push those customers to Apple's own repair services instead. It's basically a way of claiming they're making parts officially available while in practice not doing so, because they're only available at uncompetitive prices.