But that's true even on the desktop if we talk about browsers, and yet we do use extensions, ironically to augment the browser's security too.
While I do understand your point about rigorous review for a mobile app, I think that browsers should get special treatment in this regard and allow extensions.
For some reason, this surprises me. I have seen countless calls for Apple to be more open in general (do not want), but your suggestion would only open it up to other browsers. I'm intrigued and torn: I feel like Mozilla might have something to contribute there, but I feel like Chrome would follow on by wanting their own App Store.
I think I agree that Mozilla Firefox using its own engine and extensions would be a valuable app. I'm not convinced I would want to let anybody else in.
So, why doesn't everybody get to decide for themselves? It's pretty obvious that opinions differ, so people should be able to modify some simple setting on where their preferences lie in this respect. "locked down", "open for selected classes of apps", "open" or something like that.
For me, "locked down" is a choice I make when I buy an iOS device. It's not something I look for in servers or desktops, but in tablets and phones it is very much something I appreciate. Many people have other philosophies from mine: fortunately, so do many other computer vendors.
Apple doesn't blindly extend trust to app vendors - neither do I, particularly. Apple doesn't trust most folks to decide whether to trust an app vendor - neither do I, particularly.
While I do understand your point about rigorous review for a mobile app, I think that browsers should get special treatment in this regard and allow extensions.