Savage Worlds was one of the first rpg's I tried and its still my go to system for one-offs because of how easy it is. That being said FATE has completely changed the way I run rpgs and I try to use aspects in most games I run.
The reason why generic rpgs are so powerful is that you can pitch a game based on what your players want without having to worry too much about them learning something new each time.
Universal systems aren't perfect though and they're definitely not "universal". Just because you can run something in FATE doesn't mean you should. FATE relies on its games having a pulpy feeling to them. Instead think about the type of game you want to play: high action, investigation etc. and then choose a generic system. FATE can run investigation but something like Gumshoe would be a better choice.
Maybe instead of generic systems these rpgs should be called theme-specific rpgs.
One part of choosing an RPG is what system to use and the other part is what setting to use, which is a topic for another time. You may think “Well why don’t I just use the system meant for that specific setting”. You can and if you like the rules by all means do so ;but what if that setting has no rules or your favourite TV show doesn’t have an RPG published. Then perhaps finding and choosing a generic or universal system may just be what you need. What do I mean by a generic system? A generic system is a rules set that isn’t tied to a world or campaign setting. Think less of a history text book and more of a math text book.