@BraveHeartedHero, yeah, it could happen. I assume someone put that harem tag there for a reason, but calling the current situation a harem would be misleading.
I think these characters are refreshingly selfish. It's more realistic and gives them depth. Their characters really distinguish this from the usual manga and there are plenty of funny parts. It's also important to realize, they're not really bright enough to capitalize on their good fortune, which is a big part of the comedy. If they were smarter, it might be harder to laugh and root for them.