Upshot: You use quantum mechanics to decide a classical potential for you (e.g. you chose the classical potential that factors into pairs such that each pair energy is 'closest' in the Hilbert space metric to the quantum rest) - Downside: You're missing the variance.
Couldn't the quantum mechanical state become multimodal such that the classical approximation picks a state that is far away from the physical reality?
And, couldn't this multimodality excaberate during the actual physical process and possibly arrive at a number of probable outcomes which are never predicted by the simulation? Is there more than hope that that doesn't happen?