Fair question.
Only the most serious of injuries result in the horses death. On course vets do everything possible to save an injured horse Saint Are who was injured in this years National was treated on course and transferred to an equine hospital for further rehab.
The problem with horses is that they have fragile limbs and heavy tops which puts great pressure on injuries. They are also restless, active creatures who won't keep still for any length of time while their injury is recovering. There's also complications caused by them shifting weight onto their functioning limbs while keeping weight off an afflicted one.
Articles like this one describe it in better detail than I can.
https://animals.howstuffworks.com/mammals/broken-leg-horse.htm