Do you honestly think its impossible?

When I was in high school, I co-oped on a farm who had a mare who had broken her leg when she was 10. She had been an eventer and was going prelim. Well she hurt herself in the field one day, it was a clean break so they slowly nursed her back to health. She doesnt jump any more, but she does 3rd level dressage and wins consistently.
So yes, a broken leg can be fixed and the horse can have a full (or close to it) recovery.. but I think it also depends on where the break is and what it is (multiple or just one clean break)

The problem with fractures is that you need to rest the fractured site. You cannot tell a horse to use crutches and stay off the leg and the problem with full body slings is that you have to deal with laminitis because the horse is not on the leg.

Depending on the fracture location and the severity, in most cases it is not worth the money to fix.