That depends also of course on how expensive is to compute the forces relative to updating the lists. In MD simulations updating the lists is relatively expensive, and also much harder to parallelize, so that is avoided.
That can be done if the particles move only slightly at each time step. But since the distribution of velocities has a tail (the Maxwell-Boltzmann distribution), there is no hard guarantee that the particles do not move too much in a given moment. That happens, and simulations eventually crash.
I don’t think I am at a spot currently where I can use these slightly changed formulations, but I have bookmarked your post with a reminder in a few months.