Yes, platonic relationships can flourish between the sexes. I have a few guy friends and the thought of it being anything more than that doesn't happen by me. In general I think it's more difficult for the guys to keep it platonic.
Men want to nail anything with a pulse. So no, men cant be just friends with women . Women, can be just friends....up to an extent. Ever see the movie "when harry met sally"?
like i put in another thread, i asked a girl who is just a friend if we could do some fun sexual stuff, and there wasnt even a discussion, just alot of fun.