Something rules-light, written by people who genuinely enjoy all thee trilogies and th ancillary stuff.
It cannot be stressed how important this is. If you don't love everything that Star Wars is, I don't trust you with making a fun game based on the property.
For me, Star Wars is the most cinematic of franchises. Story and style trump realism. It requires a cinematic/narrative-focused game system to properly complement it. Personally, I think FATE is the best fit. Especially when you consider the built-in mechanics to level out characters of differing power levels.
Any system should be relatively streamlined and fast-playing. Star Wars, with its pulp origins, is supposed to dynamic and dramatic. You're off to a cool new location every 15 minutes. Any system that takes an hour to play through a combat is a non-starter for me.
I also think that this is the right way to go. And there genuinely hasn't really been a Star Wars TTRPG that has really managed to capture this feeling, not even the OG d6, as much as I loved and still love it. That said...
I'll stick with what I've got in that case, thanks. I really don't like FATE,
Yeah, I'm not a fan of FATE at all. I don't know if it's a thing that flows more smoothly over time the more you get used to it, but I found it so incredibly clunky and absurdly crunchy for a "narrative-focused" game.
and in general any system that strongly uses mechanics for, as you say, "story and style".
This I can't get behind, though; give me story and style over basically anything else. I'm too old and life (and the extremely limited amount of time I have to game) is too short to worry about anything than having fun with my friends while they get to do a bunch of extremely cool stuff, and that's basically Star Wars.
That's not to say I don't think there's not room for a crunchy Star Wars TTRPG experience; just that, as you say, there's plenty enough of that as it is out there, so those looking for that can "stick with what [they've] got". SW5e in particular I think perfectly captures that feel.
My default answer to "who should develop [X game]" is generally going to be Mongoose, but their games also tend to get a little too thick around the fiddly bits. Still, I'd love to see them get a shot at it anyway.