TOS only lasted three seasons on NBC, true, but then it was rerun in syndication forever, which is when it really caught on.
Granted, this is partly a generational thing. I suspect that TNG will get rebooted eventually, when the people who grew up on that show are running the studios. All you really need is one Big Name director or producer, with plenty of clout, to decide that his dream project is a new version of TNG and, voila, you have a green-light. (I believe that's basically why a new DOCTOR WHO finally happened, after the show had been off the air for a generation or so.)
But note that when Nimoy died, it was front-page news all around the world. I lost track of the number of tribute magazines I saw on sale at grocery stores, supermarkets, drug stores, etc. Not just sci-fi specialty shops, mind you, but the check-out aisle at the grocery store, next to PEOPLE magazine and TV GUIDE. Spock at least was definitely known to the general public, not just us hardcore Trekkies.
And let's not be too quick to dismiss the general public. Star Trek is not just for the hardcore Trekkies and never has been. We need to appeal to general audiences, casual fans, and newcomers as well.