It isn't just that; we are no longer a slave to Network TV. When those shows came out (I'll exclude TNG, because it went straight to Syndication, meaning it had no major network channel backing it), we were at the mercy of the networks not only finding a slot for them, but for them to fill that slot with something for an extended period of time, let alone including their time for advertising. So we had the 13-25 shows in a year, including the ads for it, for them to make their money.
Now with the glut of avenues to watch it, we are no longer slaves to that old model, and the networks know that that model is a losing battle. Look at how many shows are now on any major network, and the quality of those shows. In all honesty, I haven't watched anything on network TV since Heroes, and probably never will. I can see where 10-13 episodes for a season would be enough, because they are going to be binge watched now instead of waiting for a week, or even an entire season of reruns while waiting for the cliffhanging end-of-season show to resolve itself the next season.
As for the shows being appreciated more, The good thing about ST is that it ages well. I can only think of 2 episodes that didn't age well, and they were both in TNG: Code of Honor (already discussed), and The Neutral Zone. In the Neutral Zone, there is a scene where Sonny Clemmons (one of the guys brought back from the dead via cryonics) thanks Dr. Crusher for her work, tells her that she is "the prettiest little doctor he had ever seen, then gently smacks her behind/pinches her behind.
That... would definitely not fly today. But everything else from those classic series (TOS, TAS, TNG, DS9, VOY, ENT) all have aged very well.
BL.