It's a storytelling format that also needs to function as a reference document. It's very efficient for its requirements.
There's also the idea that one page = one minute of screen-time, but this is a bit of a red herring. Rather it's that overall a 100-page screenplay, if it contains a conventional balance of action and dialogue, with conventional length of scenes, shot at a conventional pacing, will likely result in a 100-minute film once edited. ALL IS LOST is 32 pages and 105 min film, THE SOCIAL NETWORK is 164 pages, 120 min film.
(Source: I took a screenwriting class when I was living in LA. If you live in LA long enough and you don't write a screenplay they kick you out.)
(Here is the screenplay I wrote, in case anyone is interested: http://flownet.com/ron/control.pdf)
If you think about it, the screenplay is a form of source code (or at least a form of specification), similar to a printed musical score.
Also, it's a bit easier to read in a hurry. Films and TV are almost invariably shot out of sequence for logistical reasons so actors and production crew are constantly consulting copies of the script under less than ideal reading conditions.