0 On Lightweight wheels and Forks

The lightest wheelset out there threatens to destroy the sub 800 gram mark, top end forks with steerer tubes cut to size will be about 250 grams.

We know that low speed stability of bike is aided by inertia of the front wheel, and whatever is attached to it.

So then, I'm curious to know if super light weight wheels and fork on top end bikes won't affect low speed stability, will you wobble all over the place?