Depends on how much airborne "stuff" you have around....the only downside I know to removing the cover would be keeping the bottom clean. Also, once the cover comes off people (like kids) are more tempted to get in. If you're prepared to deal with that, I don't see any reason not to remove it.

You could put a puck in a floater, but I would make sure that it stays away from the sides of the pool so that concentrated chlorine doesn't bleach your liner.

Janet