Usually climbers who do lead climbing have a lot of experience indoors and on safer routes before moving onto ones like "El Capitan", so their reflexes are properly trained.

Also a lot of the impact is absorbed by the belayer and by your feet. The way your center of mass is situated and the fact that you're almost always facing the wall helps guide you feet first. There is a limited distance between the points where you clip in, so the distance isn't too big.

The only injury I ever got while lead roping* is a strained finger, so its not as dangerous as it seems If you have proper training and user the proper equipment.