I think the troubles with split-screen are due to perspective, not resolution or performance. We all know there were many 4-player games on N64, but most of them were either FPS or standard racing games. Both genres involve the player looking and moving into the distance. In other words, reducing the display to quarter-size doesn't change how far each player can see, just the relative size of everything, which our eyes and brains are built to interpret anyway (hence perspective and depth perception).
With a game like Excitebike, there are probably two ways to implement split-screen:
1. Crop the view, keeping the racers and track elements roughly the same size as before. This severely limits how far the player can see down the track, thus affecting gameplay in a negative way.
2. Shrink the display, keeping the same "draw distance". The problem here is that the standard Excitebike view is already bird's-eye, with racers and track elements appearing fairly small in single-player mode. Reducing the size of every visual element to half or even one-quarter of its original size will make the game very difficult to play, because it will be hard to distinguish different objects and racers on the track. There are probably some visual tricks, like glows and trails, that could be implemented to lessen the impact, but then the game's presentation will be more abstract and less identifiable as Excitebike.