@Mous It (kinda) exists actually.
Look for Shadowrun: Anarchy. It's a total stripped down ruleset that's a lot easier to throw together, is streamlined for storytelling rather than finicky details, and feels positively FATE-like.
The long-running Shadowrun campaign I'm in has gone from 4th, to 5th, to Anarchy, and have enjoyed Anarchy quite a bit. It's so much smoother--for one, the GM doesn't have to pause the game every 5 minutes to look up mechanics. :-}
@Mous Pretty decently! There's no initiative rolling anymore, the order is just fixed by the GM. Everyone just rolls for things like weapons or hacking or whatever needed, then defense if there's return fire.
Physical, matrix, and astral are still separate realms thematically, but in combat it's just handled as another type of action someone is doing, so it works out decently.