Sure, iOS is a mjor player, but it also has major licensing. It's a question whether or not apple would even allow you to use Qt in your own application without approving it (and they would have to approve each and every version, no doubt) as they used to (don't know if they still do) have a ban on libraries which duplicated functionality already in the iOS (basically, you were expected to use the builtin UI libraries).

Heck, I remember when Apple clearly stated "If it isn't written in Object C, it will not be approved for the App store.", and "If your application is capable of browsing the web, it must use the iOS WebKit framework and no other", and don't forget about the rule that states you application may not interpret or compile code locally, so goodbye QtScript.