I see both sides of this issue. On one hand, a bespoke system for a particular game can really bring home the stuff that's particular to that game. For example, decay is a major theme in Mutant: Year Zero*, and the resolution system brings that home with the way pushing yourself can lead to your gear and/or you yourself breaking. And in Castle Falkenstein, you are supposed to play nobles and other characters "of quality", and of course that sort of folk won't play with something as common as dice – no, you use playing cards as randomizers.These days I have little interest in universal systems. With a few exceptions (Mork Borg's system for example, which while it does different genres, unifies them with a very specific aesthetic), I'd much rather a system designed to do one genre or milieu well than one that does multiple with less specificity.
On the other hand, a universal system has the advantage that once you know how to play it, you don't need to learn a whole new system if you switch campaigns. If you can play Savage Worlds Deadlands, you can play Savage Worlds Flash Gordon or Savage Worlds 50 Fathoms. You might need to pick up some new twists, but that's easy compared to going from D&D to Traveller.
And in between, you have the "house system", where you publish different stand-alone games using variants on the same core system. Both Star Trek Adventures and Infinity the RPG (and a bunch of other games from Modiphius) use "the 2d20 system": roll 2d20 separately vs a target number and count successes, spend various points for extra dice, additional successes can either give an improved result now or be banked for later, and the GM has their own pool of points to spend to cause trouble for the PCs. But the stats are different, the way critical successes work are different, the way you make PCs are different, and the games have different subsystems for various purposes. Someone familiar with ST:A would have an easy time learning Infinity, but you couldn't just bring things over from one game to the other.
* Year Zero has turned into more of a house system for Free League, but the original system was bespoke for that particular game.