The question for me is mostly:
"What sets F-Zero apart from other racers?"
For me, it is, primarily, that F-Zero has 50+ characters each with great character designs and their own backstories. One of my favorite things is how as a result, F-Zero has fans have a favorite character that they represent. Kind of like in real life how you find people wearing sports jerseys of their favorite team; it's interesting meeting people who are big fans of, say, Antonio Guster and hearing what they like about them. This is especially cool on sites like Deviantart, where fans of specific characters tend to specialize in art of said characters. Let me be clear though: The backstories for a lot of these characters aren't that great, but they're good enough in most cases to raise a player's interest on that front.
Aside from that, a HUGE factor behind me loving F-Zero is the fact that it is a game of strategy and preplanning. Lots of preplanning. What do I mean? Well, the implementation of side and spin attacks add an element of strategy to the game where you can play a style of being an 'F-Zero imperialist' as I've always called it, working your way up the standings via retiring mass amounts of racers. Additionally, it leads to a lot of cases where a rival might be tailing or leading you by about 2 points, that's where the strategy comes in. Do you hunt your rival down and try to retire them? Or do you simply focus on the race and hope the rival stays behind? THAT's the kind of strategy you can only find in a game like F-Zero, not Mario Kart, with all due respect. On that same topic, the energy meter is a brilliant system in that you have to be conservative with your energy and grasp an understanding of how many times a lap you can/should boost. Even then, there's more complexity added in the sense that how many boosts you can fit in per lap really comes down to which machine (or custom part) you're using.
In my eyes, F-Zero cannot be properly succeeded by another title until it replicates the same level of high speed racing, possible strategizing, and many unique racers + backstories. F-Zero hits the nail on the head on all fronts: Speedrunning, casual play, lore, fan art. Perfect game.