Not entirely sure about the cat flap open all the time idea. It is true that cats want it that way, but - outdoor cats can be in danger of cat haters (one of mine has a permanent pellet lodged in his thigh); traffic (I had one cat injured that way) and getting lost (again, this happened, although I suspect that one of his admirers had decided to take him for a walk and he escaped).
Also, cats are hunters, and sometimes they hunt endangered species. I lock my cats in at night, but I believe that the most dangerous time for hunted animals is dusk and dawn - that is when most cats do the hunting, rather than in the hours of total darkness.
You cannot train cats, but you can restrict them in their own interests.