Because their platform, their rules? IDK, I think it's perfectly acceptable to limit what you can do on someone's platform, since after all allowing anything on your platform will cause a lot of crap to appear - like a lot of stuff on the Android platform before it changed to the Play Store and Google started being a bit more strict about using their platform.
Restricting what developers can and cannot do on a platform allows Apple to give more guarantees and reliability in terms of performance and battery usage, as well as security and stability. Those are the primary reasons behind Apple's restrictions on the iOS platform.
You are only partially correct in your analysis. Yes, controlling the platform can lead to a better user experience. But how does banning browser engines lead to better app quality? It doesn't. If you look at the history of app store restrictions, you'll find that any app that provides an open platform or programming environment has been banned. That is because it takes the control out of apple's hands. It's a power grab.
What are the performance, security and stability benefits of removing native print-to-PDF functionality from iOS? It was supported by Apple in early iOS releases.
Restricting what developers can and cannot do on a platform allows Apple to give more guarantees and reliability in terms of performance and battery usage, as well as security and stability. Those are the primary reasons behind Apple's restrictions on the iOS platform.