As a screen reader user, Apple does have a first party screen reader, VoiceOver, and does indeed not let you run a third party one. In fact, it does not work well even on the more open MacOS. So essentially it's VoiceOver or nothing. Luckily, especially on iOS, VoiceOver mostly works well.
I'm glad it works decently on iOS, at least. my mom has little central vision, and she struggles on iOS just using high contrast plus scaling plus magnifier. I think she has just enough vision to not absolutely need VoiceOver but it still makes using her phone a frustrating and tiring experience.