Because people would do something stupid, get themselves in a mess and then be all over social media blaming Apple, which would potentially damage their image (which they are fiercely protective of)
Apple have always taken a “we know best” approach with iOS whereas Google have been more pragmatic with Android.
I can see arguments for both approaches but I do believe Apple should be able to apply the rules they want on the platform they developed: if a user wants more freedom and control, there are plenty of other phones on the market
I'd like to point out that the "plenty of other phones on the market" argument no longer applies. Google is starting to exert an Apple-like amount of control over devices from any vendor -- whether it's their hardware certification program, moving of core OS functionality into the proprietary Google Play Services application, or SafetyNet jailbreak detection system. This means that, software-wise, there are now effectively only two platforms. This is, as traditional economic wisdom would say, bad.
I am personally of the opinion that this situation is exactly what government regulation is designed for. However, I don't know whether it's a better route to force Apple and Google to not screw over their customers, or to force more competition. The second route would normally make sense, but then again even Microsoft (with their mountain of cash) tried to compete and failed miserably. It's a pretty nasty situation in all respects, especially since users aren't really noticing their options being gradually taken away. I really didn't mind Apple doing whatever it wants to its customers in its own little world, until it became part of a duopoly with Google.
And sure, Apple and MS may have practically had a duopoly on the desktop OS market for years. The difference is that MS never locked down its OS, and you can still sideload all you want. They have tried to follow suit with their Store and locked down OS versions, but in the desktop world the status quo is freedom so they failed. Nonetheless, with Windows 10's slow-burn feature updates they will eventually succeed in gradually taking away control from their users (eg - the Cortana off switch, which gradually became more and more hidden until it disappeared).
I might also add that I previously considered Apple's "safety and security" argument against sideloading to be BS, and I still do, but I now see one small way in which it can help the consumer. Indeed, a company like Facebook is big enough that it could probably get users to sideload its app and thus skirt a lot of Apple's surprisingly nice new privacy features.
