Why write more back story than what will end up in the movie?

I keep hearing about directors or writers talk about how they “develop” a story or a character by writing a back story.

VERY IMPORTANT:
Lets assume that the script/story was/will NOT become a novel/book/comic.

Wouldn’t a few sentences be enough to “motivate” the actor and/or just to describe how/what the character is?

Having hundreds of pages of additional story on wiki pages does not really serve any purpose if it will never end up in the actual story that people see.

Wouldn’t you, as an artist/filmmaker, want to include everything you put into a character on screen?

There are a lot of popular movies that have so many additional stories that describe the rest of “this world” the author created, including creatures/plants/characters that you never end up seeing in the movie.

Again, lets just assume for a moment that none of this is meant to be translated into a video game/action figures/comic/playing cards etc.

Hope my question makes sense. (I think I haven’t completely lost my mind…yet)