Pardon me, I think you misunderstand what I claim they have a monopoly on. They (obviously) don't have a monopoly on the mobile(or mobile software) market. They have a monopoly on the iOS software distribution market(a secondary market spawned by apple themselves). On an iOS device you cannot install a different App Store, therefor the end-user has no other choice than using Apple's App Store to download/buy software(=monopoly).

TL;DR iphones don't have a monopoly, the _AppStore_ has.

On Andoird the situation is a bit murkier, you technically can install software from outside Google's playstore, but you have to click trough scary dialogs(warnings about the danger of doing so), and App Stores installed that way don't have the same device permissions than googles play store have(you have to manually confirm each software update, for example). so yeah, on android it's debatable, but that's a story for another time.