History doesn't show them to have had to drop many restrictions; I don't see why that would suddenly change. I've always thought that it's hard to come up with a killer app that would run afoul of the guidelines that's not outside what Apple's trying to make their devices good at. I think the record bears this out. I don't think that's because Apple is co-opting so much stuff, it's because their guidelines allow what the overwhelming majority of useful apps need in order to be useful to the overwhelming majority of people. (Because most people want devices that are good at what Apple tries to make their devices good at.)
It's easy to come up with an idea for something cool that requires access to capabilities that aren't permissible in the App Store (constantly running in the background, access to execute downloaded/arbitrary code) and it'd be a horrible shame for there not to exist devices that can do those things out-of-the-box, but the fact that they've so far been forced to bend very few of the rules implies that there's proportionately very little demand for such things.
That's some pretty twisted logic there. By that logic, if Microsoft had banned other browsers from appearing on Windows then because no other browser ever shipped for Windows that would be proof there was no demand for other browsers? Really, that's your logic?
The fact that useful alternatives with possibly better interfaces and/or better features (not just more but better) is something we'll never know if there is a demand for because Apple bans them before we get a chance to know.
Maybe a Hypercard for iOS would take off but apps that make apps are banned. Maybe an Amazon music store or a Google Play music store or a beatport music store would take off but apps that sell music are banned. Maybe a browser that is faster, or more secure or provided more features would take off but we'll never know because they're banned.
We really only have 2 data points. Windows and OSX. As far as I know on both OSes the browser provided by the OS provider is used by fewer users than other browsers. I don't know what the numbers are on OSX but even if Safari has the highest percentage (doubtful) if Firefox+Chrome+Others have a higher percentage than Safari that would still mean more people are picking something other than Apple's offering.
My point was not that there's no demand whatsoever nor that no disallowed apps might ever take off if they were to be allowed, but simply that Apple doesn't feel significant pressure from their customers to reduce their restrictions and I don't see that changing.
It's easy to come up with an idea for something cool that requires access to capabilities that aren't permissible in the App Store (constantly running in the background, access to execute downloaded/arbitrary code) and it'd be a horrible shame for there not to exist devices that can do those things out-of-the-box, but the fact that they've so far been forced to bend very few of the rules implies that there's proportionately very little demand for such things.