I think people tend to overestimate the desire of most cats to spend time outdoors, because as humans we ascribe human motivations to cat behaviors. So we see the cat repeatedly try to go through the door, and we think of this as persistent behavior that reflects a high degree of motivation to go "outside". But "outside" is not a concept that a cat really understands. They understand doors well enough, and they might be frustrated and upset by not being allowed to go through them. But, as you mentioned, there's actually a lot more for them to be frustrated, upset, scared, and injured by outside than there is inside.