I haven't seen the precise wording of the agreement, but I have talked to multiple "authorized repair center" owners, and my understanding is that they can only

I haven't seen the precise wording of the agreement, but I have talked to multiple "authorized repair center" owners, and my understanding is that they can only replace batteries on iPhones, and even then they must submit the serial number of the phone to Apple and wait for Apple to ship them a battery. That's an awful deal compared to third party repair centers, which can stock batteries, replace them quickly, and warranty the batteries themselves if a customer has issues. As far as software issues go, we really only get two of them at our store: either someone is out of space on their phone, or their phone won't install the latest iOS update. (We got a million of the latter when iOS 9 came out.) There's not much money to be made with either of those two issues, and they're both relatively rare compared to broken screens, so even if they are allowed to fix software issues, it's certainly not a money maker for them. Unfortunately for these businesses, being an authorized Apple repair center doesn't exactly bring in the big bucks these days. Strange that Apple won't do an entire program for screen repairs--it'd certainly make them a killing to do so--but it's their prerogative, I suppose.