I've checked a box multiple times with no issue. I usually tie a luggage strap around it for some extra security but really to provide some sort of handle for myself when I am carrying it out of the airport.

As for shirinkwrapping, when I was in SIN, I actually saw a kiosk where they offered to shrink wrap your luggage for a small fee. I guess its for extra security eventough inspectors may need to cut it open.