I don't think TNG was "cut short" - seven years is a very healthy run, it finished while it was on top (which is far better than running and running into obscurity/indifference from viewers) and it left the audience wanting more. Now, how Paramount then went ahead and gave that audience "more" - that deserves a little scrutiny I think.
Quite simply, we got too much Trek in such a short space of time. Here's how I, with hindsight, would've paced things:
1987 - TNG starts
1993 - DS9 starts
1994 - TNG ends
(only DS9 for this period)
1996 - First TNG Movie Released
1998 - Voyager (or different spin-off) starts
1999 - DS9 ends; 2nd TNG Movie
2002 - 3rd TNG Movie
2005 - Voyager/spin-off ends; 4th TNG Movie
2006 - Enterprise (or a different spin-off) starts
Just eases out that overkill/franchise fatigue we experienced from circa 1995-2000. Don't get me wrong, I wasn't complaining at the time, but in retrospect it was clearly responsible for the drop in quality/audience indifference.