While not really required, they really do help with controlling a lot of the twitchier machines like Death Anchor or Cosmic Dolphin. Just let you get very precise turns in a way that a full press probably wouldn't. For more balanced machines like Blue Falcon or stiffer machines like Hyper Speeder, they don't really make much of a difference but it's still just an extra bit of control that's nice to have.
It's the only F-Zero game with analog strafes, so it would definitely work without them, but it'd be a bit of a shame if they just removed analog trigger support when Switch games can still look for that, like Mario Sunshine or whatever Trials game is on Switch. Definitely not a deal breaker, but I hope it keeps GC controller support.
Oh also (EDIT) you can actually remap all your controls in GX so you can already test non-analog strafes, and I'm pretty sure acceleration and braking also becomes analog if you map the triggers to it. There's just no reason why you would want to go less fast.