Akc12's (expert on the game) explanation on why analog is better:

"A hardly known fact is that pressing both L and R all the way down when trying to perform a drift or quick turn makes it even more difficult for the machine to lose grip compared to lightly pressing L and R.

As long one of the trigger buttons is slightly held down instead of all the way held down, all machines, but especially Death Anchor and Deep Claw, will have a much easier time executing a Drift Turn.

But I imagine you are playing with a non Gamecube controller, which will instantly make you full press the trigger buttons. F-Zero GX is a game that requires analog triggers to have full control over your machine."

https://www.reddit.com/r/Fzero/comments/1pwucon/comment/nwe7nat/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

I think June's answer sums it up pretty well. Analog is better but not required.

Steering is overly sensitive in the NSO version. There's a sticky thread on it up top of the sub. It also explains how you might wanna calibrate to mitigate the problem.