There is no need for a disturbance in asteroid belts for asteroids to hit the earth. The orbits of asteroids are in general not stable. There are currently som

There is no need for a disturbance in asteroid belts for asteroids to hit the earth. The orbits of asteroids are in general not stable. There are currently some >7000 known earth-orbit-crossers, which, if their orbits would not be modified by something else and given enough time, would all hit us eventually (except one which shares our orbital period). And that's really just scratching the surface, as we still haven't mapped but a small fraction of asteroids. The sky up there is still really chaotic, as space is really big and ~5B years is simply not enough time to produce a stable equilibrium.