I think to help kids appreciate something classic you have to give them a little historical context. And you can say while they didn't predict the DNA thing here are a few things that the series did predict.
Being a father of three, I can tell you it simply isn't that easy.
I will make concessions for TOS that I simply won't make for most other things I watch. Society is different and so is technology. We're expecting today's kids to make the leaps we do and then say they have ADD when they can't or don't want to do it. Which simply isn't fair to them (some do make the leap which is cool).
Would TOS make the same impact on me today if I was an adolescent? I honestly don't know as there is much more competition in the world today.