> You might see it slowing down first, and you start slowing down, or continue because there is enough distance anyway.

That's the thing, though - if you were already at the distance limit, and the car in front of you starts slowing down, you have to also start slowing down right away to maintain said limit. If you do not, then it's already "not enough distance" by definition at that point, and you're the one responsible for that.