Short Version: I generally feel that mechanics are much more important to address the type of story and/or table experience you want to have. Settings are generally just trappings on solid, flexible mechanics.
For example, Blades in the Dark is a game about running a crew of thieves (or assassins, or a variety of unsavory types). Its mechanics are centered around a cycle of "jobs" or schemes and building your crew's territory/power. The game comes with a fairly evocative setting in an industrial, post-apocalyptic, slightly magical city called Duskvol. However, the mechanics themselves aren't terribly tied to that, and if you replace the setting information with say...a space setting...you can get something like Scum and Villainy pretty easily. So, all the setting information is basically what I would call "Trappings" around the mechanical architecture. If you want to run something like Peaky Blinders, but in a different world/setting, use the Forged in the Dark system. You just need to create a new set of Trappings to go with it. I would not want to run the main Star Wars arc using the Blades in the Dark system, but I could certainly see running a game in the Star Wars setting using the system. It would just be more like Solo.
I actually feel like this is a common oversight/failing for many "universal" systems. For example, Savage Worlds. Yes, you can run Savage Worlds with whatever trappings you like. But the Savage Worlds engine serves a certain style of adventure-story or maybe table experience. If that's your bag storywise, you're golden. You can run it in whatever setting you like. So long as it features fast-moving combat with mostly human-scale participants, you're good to go. However, that doesn't mean it would be good for say, running a police procedural.
Some other systems/games and my thoughts:
Fate - pretty easily does the proactive and competent heroes save the thing thing, as it set out to do. Fairly easily modded or extended to other story-genres. Doesn't do gear-porn, spell-porn, any-kind-of-list-porn or super-specific tactics well (although that is sometimes argued). Story/character arcs wobble all over the place, if not carefully tended.
Gumshoe - mystery/investigation mechanics at their best. Can do "thinky" stories. Extendable to add more "action" and list-porn, but seems kinda clunky at it. Story arcs tight, character arcs, not so much.
PbtA - highly variable with implementation, but highly tweakable. Subtle but profound focus on character arcs in some implementations. Robust in the right GM/developer's hands, but tricky to implement.
GURPS, Hero, several other 20th century universals... - Trappingless, but somehow manage to lock in play pretty well anyway. Point costs seem to depend on a certain play-experience outlook and easily break when taken outside that. Story and character arcs must be hand-held, if present. List-porn lovers dream.
Cortex+ - Highly variable, depending on which mechanical subsets you choose. To the point where I'm not sure how much of a "system" it is, so much a kinda-nifty dice idea that can be applied in a lot of ways. Some implementations do relationship drama really well.
D&D, D20, most trad games - 2D sidescrollers brought to life in 2.5D in full color-ish descriptions. Fantastic for list-porn lovers. Variable for tacticians. Character arcs all bend up, up, up! Unless they come to an ignominious halt. Story arcs, totally optional, depend on GM implementation. Adventure arcs common.
Side notes:
On the design side, its pretty hard to create a list-porn system without "baking in" an exploration story-setting to some degree. That's kinda the point of lists.
Almost any system can be used to do any genre...if the GM and players bang on it hard enough. However, that doesn't mean you should use a hammer to put in screws.
