1) Dominating a market is not a monopoly. There are other choices that work just fine for 45% of the US population, and more worldwide.Not fair comparisons. Neither McDonald's nor Burger King dominate the "fast food" restaurant market like Apple dominates the mobile OS market. Apple's iOS (and therefore the App Store) has around 55% to 60% share in the U.S.
Also, this is not about Apple and its own apps like Pages, Numbers, Keynote, GarageBand, Safari, etc. No one is saying here that Apple should have to make Pages, Safari, etc. available on Android or anywhere else. Apple is free to only offer those apps on Apple devices.
2) Apple got to that market share from 0% by offering something different, competing with established players
3) The "something different" defining iPhones is the walled garden iOS ecosystem, which has never allowed sideloading.
4) iOS is Apple's own app. You're saying Apple have to modify iOS to allow alternative app stores. How is that fundamentally different to saying they have to modify Pages or Safari?
5) jailbreaking iOS violates DMCA, but I don't think there's anything stopping anyone from developing their own OS from the ground up to run an iPhone.