SF shows are, if anything, usually pushed off the air *before* their prime. Not sure why you think they all go on too long. It's pretty rare for any of them to make it past 2 seasons without a major retool, and then they die in their third if they get there. Most of the exceptions end around season 5 with only Trek and Doctor Who really pushing beyond that barrier.
As for pushing Berman off, well, the BBC managed to push producers off Who even in the heyday to make way for new blood. Granted that the last people in charge did a major fuck up job on the whole thing that killed the show for a decade+. But the thing is that in both Trek and Who's case, the break only served to allow new blood to take the reigns. It wasn't the break that was needed, it was the new blood.