The only problems would be speed and memory.

There is a tiny chance that when he said "does not reproduce the causal structure of neural interactions", what he actually meant was "would simulate the neural interactions extremely slowly", but if that was the case, he really could have said it better.

My priors are that when people without formal computer science education talk about brains and computers, they usually believe that parallelism is the magical power that gives you much more than merely an increase in speed.