F-Zero was fun, I spent a lot of time on it. I really liked to find shortcuts by boosting just before a jump and trying to land on a completely different part of the track. But it was so annoying that you couldn’t outrun other opponents. You could do the perfect race, but if you made the slightest mistake in the last lap, the 2nd would be right there on your tail.
Indeed, in that case "rubberbanding" doesn't quite describe it as it involves giving a boost to the laggards (e.g IIRC in Sega Rally 1v1 second-ranked car max speed would get a very obvious +20kph plus a slight boost to grip).
Instead it might be the most egregious case of quantum tunnel rubberbanding: you could cut a ton of corners and they would still be right behind you, I presume the opponents don't run the course at uncapped speeds but are instead hard-warped right behind you every so often, with the illusion preserved as you can't look back when you move forward (although there's a map but it's mostly a progress bar and most of - all? - the time it shows only you).
Would be interesting to rev-eng the code implementing it or even have some PoV hack to witness it first hand.
You can outrun them on GBA though, the opponent is visible on the map:
