Okay, so who "owns" the Doctor? Who "owns" James Bond? Who "owns" Batman? Dracula? Superman?
Many of these characters were iconic when they first appeared, but many other actors have portrayed the same character throughout the years (Dracula is the oldest). However, people will have their personal favorites. It doesn't mean they can't appreciate the other renditions, though. But it's definitely NOT the actor that makes the show. If you are saying that it IS the actor that makes the show, that means that the show is rubbish, because the story can't stand without the original actors. But I've noticed that people want the original stories, NOT the original actors, and that they are miffed that the characters were put in an alternate universe.
See, just about all of those are very unlike the Trek cast. The Doctor had changes to his character within the original series run, before the show had a chance to be digested by longevity the idea of his face, his entire persona, changing was established. It's actually an active part of the excitement of Doctor Who, that he can and will
Superman, Batman, and Bond had so many changes and iterations even early on that again, it's not quite the same thing.
Whereas with Star Trek, you had the original series run for 3 seasons, then syndication, then the animated series, followed by more syndication, then the movies. It wasn't until the 4th TOS movie, nearly 20 years after the show had first aired, that an entire new set of faces were brought into Star Trek with TNG.
It's not that Pine and Quinto can't be iconic, it's that they are not yet iconic
in these roles. Shatner and Nimoy are. If time is good to the new guys, and they get to do more stuff, then they probably will be. Lord knows they seem to be giving it their all in both movies. However, if it ends abruptly with movie three, it won't be Pine and Quinto who will continue to endure. It'll be the same ol' TOS run in syndication.