Anyway, a soul would be an entity whose existence is postulated unnecessarily if the brain itself can reasonably be postulated as the source of the phenomenon. So, what "simpler" means in this case is fewer entities (and types of entities, such as immaterial souls) that we have to invoke in order to explain something. Not that a soul is somehow more complex than the brain (how would we know?).
A major criticism for any mix of materialistic and spiritual entities having causal relations (such as the one above where someone questioned how we know there isn't a *real* out of body experience that just happens to coincide with a particular kind of cerbral stimulation) is the lack of any means to causally relate a material thing ( even a force) with something spritual. The reverse, having a spritual thing cause things in the material world, is just as problematic.