After enough time it becomes clear whether a show has elevated to pop culture icon or not. Regardless of the original ratings, TOS has many times over. It is right up there with I Love Lucy as one of the top TV shows of all time. But TNG has also become part of that club--to a lesser extent. But the other shows haven't. You can tell TNG has become immortal in the way it's used for humor on the web (Picard facepalms, etc...) and on TV (Family Guy, Big Bang Theory). Everyone knows TNG whether they are Trek fans or not. I don't think people view TNG with the same reverence they do TOS. It simply did not break as much ground. However, it is an enduring symbol of the era of the late 80s. And since the prime buying demographic is nostalgic for that era, that is why they went back to remaster TNG.
Do I think they will do the same for the other shows? It's possible, but I think it would be more of a PR move on CBS' part to please the die-hards than something they think would really pay off.
There is a halo-effect with JJ Trek. The same thing happens with old superhero properties like the Bill Bixby Hulk or any reboot (Starsky and Hutch). People become interested in other takes on the same material. I don't think the average juvenile JJ Trek fan would find DS9, Voyager, or Enterprise that interesting. They never grew up with these shows and all these shows either suffer from bad writing or deviate too far from what people like about Trek or both.
As for the movie era deviating from canon, the original production design for TOS started in what, 1964? And even then, with the gooseneck screens and things, it was very much warmed over Forbidden Planet. By the time the final episode aired, TOS had gone from looking contemporary to looking like a cartoon caricature of SF. 2001 was Trek's contemporary, and even shared an actor (Gary Lockwood) from Trek's pantheon, and yet 2001 still feels barely dated compared to Trek. (HAL even looks like it has isolinear memory ala TNG.) I've seen the Phase II screen tests and they were not advancing the look very much, at least with the uniforms, which were going to be exactly the same as TOS. By the time they got to TMP they had the opportunity to reflect how much our vision of the future had changed. The TOS enterprise was nice for its time but the TMP enterprise had a lot more thought put into it.
The hype behind JJ Trek, and I remember even Cawley being sold on this when he visited the bridge, was that JJ was making Trek feel plausible, but it doesn't. Sure, the FX are better, but the ship designs suck. Engineering looks like a brewery. They designed things to suit a particular gag or to evoke a style but not because it made any technical sense. TMP had science advisors, but I don't think JJ Trek ever did. Trek seemed to still have a mission of being "speculative fiction" back with TMP. JJ just treated the Trek property as you would a comic book one.
I stand corrected. JJ Trek had a science advisor.
You'd never know it, though.