To add on why broken legs are fatal: its because horses are so big, that even with a sling, they cannot support themselves well on 3 legs. And lying down is also not an option as their own weight will crush their internal organs if they stay down for too long.
It’s not just horses, all large mammals have this problem from lying down too long. Horses can and do lie down every day, but for short periods of time. It’s the extended lying down from illness or injury that kills them.