Not too many movies full of characters in their 50s and 60s would work with themes filled with teen angst, anyway. It was hardly the gateway movie to bring in
new, younger fans. It was a sentimental swan song.
One thing I've noticed a lot of lately is a "kids react to ___". I saw one where kids react to Jaws, and another where they marvel at an Apple II. The idea behind this is to try to quantify the change in culture between then and now.
I saw Khan when I was 12 and enjoyed it. I had already been a fan earlier, enjoying TOS reruns in the 70s, despite the obvious outdated 60s cultural context of it. Would a 12 year-old today enjoy the old stuff as much or are they so desensitized and low-attention-span that only something that moves the breakneck-pace of Into Darkness will satisfy? There's a lot of assertions from JJ fans that say as much.
What I haven't seen are actual anecdotes where young people watch the older stuff and render their opinions. I bet the info is out there, though, and if anyone has any links, please pass it along.