In many ways, wasn't TNG a "re-telling" of the original series to some extent? Yes, it did take on its own identity from around s3 onwards, but the first two seasons were very much in the mould of TOS.
The difference being, of course, that when TOS first hit the screens it was unlike anything that had been done before, whereas when TNG hit the screens it was just re-treading some old ground. Don't get me wrong, I enjoyed TNG, and there are still a few eps that I consider right up there among my favourite TVSF eps of all time (generally surrounded by B5 eps), but it wasn't really that much of its own animal.
DS9 was a different ... I enjoyed for the first couple of seasons, but then lost interest, as my interest in B5 intensified. Nothing against DS9, and not interested in the who-copied-whop arguments. I just found DS9 less and less interesting as time went on.
Voyager was potentially great, but a massive missed opportunity to the extent that within the first couple of episodes it became almost "Star Trek: The Next Generation: The Next Generation"
And I never really watched Enterprise, because I had just lost interest in ST completely by that point.
At this point, I don't think the world in general will miss ST for some time to come.