Well, that's what the GBA was capable of. Besides, it may not have been Miyamoto's call to make those games, and his priorities are probably different from what they were. If he's gonna dust off F-Zero, he's gonna do something surprising with it. Until he or some one else figures out what that is, we shall just wait.
Saw you edited your post. Adding "check list features" isn't his style. It's not about making it work, it's about adding that element of surprise. And motion controls might not be responsive enough for F-Zero.
About Mario Kart, it sells. That's all there is to it. It's fun, people like it and it sells. They aren't gonna shake that formula up too much because they don't have to. F-Zero doesn't have the luxury of producing Mario Kart numbers.
Also, Captain Falcon is a key character in the Smash Bros series. He was in the first one! Lucas was in Brawl, and Mother 3 is NEVER coming to the US. How's that for a cock tease?