1) REM sleep is associated learning new skills. We can teach experimental subjects a new skill in the laboratory, selectively interrupt their REM sleep, and se

1) REM sleep is associated learning new skills. We can teach experimental subjects a new skill in the laboratory, selectively interrupt their REM sleep, and see that their skill doesn't increase to the same extent as a control group who don't have that phase interrupted. The same isn't true with non-REM sleep. We don't really understand the mechanism though and this potentially does bear directly on the question. 2) Well, it would get in the way of actually living? If you're talking down some stairs and then your brain's motor cortex starts working on consolidating a skill and you fall you'd hurt yourself. 3) I don't think we know that. Possibly we had to sleep for memory related reasons and our bodies just evolved to use that time for other sorts of important housekeeping when it wasn't moving around doing stuff? 4) Learning is very important and takes time. In addition to the procedural memory consolidation in REM sleep we also move long term memory to a more stable form of storage in other phases. But neural nets don't really have anything analogous to a brain's explicit memory so this doesn't really bare on that.