The reasons are discussed (well, flame-war'd, and there's a lot of talking past one another) in practically
every HN thread in which Apple is mentioned, even when it's not about the store. I haven't looked but can almost guarantee there's a thread here already covering it. Allow me to summarize the last 100 times I've engaged in or witnessed this:
Party 1: Apple's store hurts consumers and contributes to making their devices not even real computers, just consumption devices, not for creation! It's a shame and they should be broken up or made to allow other app stores. It's plainly anti-competitive, and anti-choice.
Party 2: Hi, I'm a consumer, and I like that they force 3rd parties not to be shitty. I don't really care how that hurts 3rd parties, as long as Apple's big enough that the 3rd parties can't afford to turn down that slice of the pie so they keep providing me the apps I want. Also I do work & creation on iOS devices, often. So. (here party 2 may or may not concede that it is anti-competitive and they simply don't care since it happens to be benefiting them, and may or may not argue that it's not anti-choice, since without Apple's model the kinds of app store ecosystem model the consumer can choose would be reduced by one)
Party 1: 3rd party stores wouldn't hurt you, you could just not use the apps that move to those if you don't like what they're able to do on the other stores. (this is usually where insults to Party 2's intelligence are placed, and in fact this post is often mostly that, and probably also push-back on allowing other stores representing a reduction of choice, if Party 2 chose to advance that line in the previous post)
Party 2: But... right now I have all the apps I want, and none of them can do things I don't like because Apple doesn't let them. How's it better to replace this situation with multiple app stores, so I might have to choose between privacy and using the apps I want? That seems strictly worse for me. (if the which-kind-of-choice-matters argument is in play, an argument that the ecosystem of Apple's store will be harmed by adding more stores, so in fact Party 2's preferred choice of the current, non-so-harmed App Store ecosystem will be removed by adding more, may be employed)
From here things mostly just go in circles and hypotheticals and examples from Android's Play store, which probably won't be particularly relevant to the much-more-restricted Apple App Store and any hypothetical changes to its position given 3rd party app stores.