Apps get removed for the store regularly on the sole reasons of competing with Apple apps. It's not even hidden, it's explicitly forbidden by Apple rules. For instance: the Chrome app really is an extension of Safari, because it's forbidden to compete with Safari. It goes the same with every other kind of app Apple distributes.
It's even worse than that, actually: they sometimes take an app down, and then enrich their own apps with the good ideas those apps had.
For instance: remember the app that got banned, because they used the lock button as a trigger for their camera app? The reason was: the lock button is not done for that, it's made to lock the phone. Ok, fair enough. Next thing you know, Apple's camera app made an update: you could now use the lock button to take a picture with it.
Apple makes great products, but they have a very unethical way to do some things. And worse: they're so powerful that their unethical strategies remains roughly untouched in most countries.
I think if Microsoft did half of what Apple does today (with the Mac App Store, for instance), they'd get sued in a blink (although Microsoft did enjoy years of unpunished unethical stuff as well in their time, to be fair).