As far as I know, the reason F-Zero doesn’t render all the way out to the horizon is none of the potential reasons listed there.
The SNES, like most 2D consoles, uses “tile-based” graphics, where one section of memory stores small images (8×8 pixels, in the SNES) or “tiles”, and another section is the “tile map” that arranges copies of tile-images into a grid that covers the screen. 2D consoles were designed with typical 2D games in mind, so the “tile map” RAM typically only held enough tiles to cover four times the screen resolution.
Four screens’ worth of tile-data is more than enough for 2D games, which would allow the player to run around and “swap in” other chunks of the tilemap as the player drew near. However, once the SNES psuedo-3D gets involved and the background is drawn at an acute angle, the player may be able to see clear across the full width of the map and then some. What do they see past the boundary?
Super Mario Kart punted on this by designing all its tracks to fit well within the 4-screen area, so the player could look in any direction and see something reasonable. However, SMK tries to replicate go-kart racing, so cute, small tracks are a benefit if anything. F-Zero wants to provide the feeling of high-speed futuristic racing, so it needs a little more room: as you drive forward, the track you’ve just raced over is being recycled to provide the track that’s appearing in front of you.
So F-Zero’s limited horizon has nothing to do with errors introduced by integer arithmetic or the processing overhead of doing physics calculations for more cars, it’s just that no more track data will fit in video memory.