Why does it speed up gradient descent if the function is smooth?
My guess it is due to the derivative, as ReLU has a discontinuous derivative at 0. Hence if you use the definition:

$$
f' \approx \frac{f(x+\epsilon) -f(x-\epsilon)}{2 \epsilon}
$$

and $x$ is very close to 0, you will get many of those 'jumps'.