I think the basic reason that it’s hard to make an interesting QCA using this definition is that it’s hard to make a reversible CA. Reversible cellular automata are typically made using block-partitioning or a second-order method. The (classical) laws of physics also seem to have a flavor more similar to these than a GoL-style CA, in that they have independent position and velocity coordinates which each determine the time evolution of the other.
I think the basic reason that it’s hard to make an interesting QCA using this definition is that it’s hard to make a reversible CA. Reversible cellular automata are typically made using block-partitioning or a second-order method. The (classical) laws of physics also seem to have a flavor more similar to these than a GoL-style CA, in that they have independent position and velocity coordinates which each determine the time evolution of the other.