Perhaps you're right. Maybe it's entirely coincidental that Apple's policy also prevents owners of Apple devices from using a browser with modern features that would allow web apps to effectively compete with the native apps from which Apple gets a huge cut of the revenue because of its monopoly control over the app store.
Or the real reason, is as it was pointed out in the other comment, is to cripple other browser engines that offer a platform that could actually be competitive with AppleKit's turning their control over the App store (and what people are allowed to access according to their own taste) irrelevant?
And if that's the real reason behind it, its clear the end user best interests are not being taken into account, as in not having access to possible better options according to your own tastes, contrary to what a lot of people in the comments here are trying to make we believe its true.
Not letting other browsers use their own JS engine (which is what it means to 'forcing them to use Internet Explorer engine on Windows' in your analogy) is because Apple want to disallow write|execute for people's safety.