Michael Piller said he felt having Wesley quit starfleet academy was a slap in the face to Gene Rodenberry and I think it was a misstep for the character to jettison everything that defined him.
Not 100% of the timeline, but I recall thinking it was motivated by TPTB at Paramount deciding they did not want Wesley Crusher in the movies so had him phased out of the series. I do recall the Wesley-Haters were very loud and seemingly omnipresent.
Just three years would have been too brief, so much so the show would widely be regarded as failure and not very remembered even though the third season was considered the best; audiences expect successful shows to go on for a while and continue to be good while doing so. Six or seven years, though, and then not doing another spinoff until '96 or '01 would have been both a good run and a good break.
No, three seasons is enough to, if the fans loved it, to be viewed as a success (at least creatively and critically). I mean TOS only lasted 3. Paramount would still see it as a property with value.
I wholeheartedly agree that there should have been a rest period of at least three seasons between each Trek series. It used to be there'd be mindful, even fearful, of overexposure. Nowadays they just run their horses until they drop dead of fatigue.