F-Zero has been gone for a long, long time. I hate to be fanboyish about it, but WipEout has filled a big gap in the futuristic-anti-grav-racing market (at least, for me). And it's become so well developed these days (HD Fury was fantastic), adding new game modes (Zone, Zone Battle, Detonator etc.) It's really good at what it does.
But, F-Zero used to fill a different gap in the market. Races seemed faster, they were more hectic (30 racers), courses were wider to accommodate this. It was hard as nails. There were different mechanics.
What I'd like to see from a new F-Zero game is just developing more of these ideas. New game modes that work within this structure - Cat & Mouse mode that you described sounds incredibly good (genuinely, a really interesting idea). Some more stuff along those lines would be really cool to see.
I'd also like to see it with really nice online features too. I mean, 30 people racing online at those speeds would just be awesome to see.
Also, I'd kind of like to see the studio that made GX make it. They did a really good job with that game. It was one of Sega's teams, wasn't it?