Or is it merely inadvisable, because the combined measure of all the histories containing suffering is very tiny?
I'm going to go with this one.
If you decided that, for some reason, all that matters is that there is a nonzero probability, then there's nothing you can do to stop it. The amplitude will only be zero at isolated points in configuration space. Move a photon a Planck length to the left, and it will now have non-zero amplitude.
From David Deutsch's The Beginning of Infinity:
I'm not so sure we have the computing power to "simulate a person," but suppose we did. (Perhaps we will soon.) How would you respond to this worry?