There are several reasons. Horses develop problems in their hooves if they don’t move around enough or are forced to put weight on only 3 legs. You can think of their hoof as a giant fingernail, and the bone behind it is shaped like a wedge pointing forwards and towards the ground. Too much pressure on the other 3 hooves can cause severe pain, swelling, and separation of the bone from the hoof. In severe cases the bone in the hoof can puncture through the bottom or separate from the top.
So then you might ask “why can’t we make them rest while they heal?”
Well horses can’t lie down for a long period of time. Not only can that negatively affect their hooves and muscle tone over time, but the pressure from their own body can restrict blood flow.
Within 2 to 4 hours of a horse not being able to move from one side, they can develop muscle and nerve damage. In surgery, horses are often kept on giant foam pads to help reduce the pressure on their body. Keep in mind bones take months to heal. A horse cannot realistically be on the ground to wait for that.
The other option is a sling for the horse to stand stationary and upright while it heals. But this creates challenges with pressure sores and excessive pressure on their breathing.
There are other issues including dietary concerns and gastrointestinal effects, but in short, it is very very hard to heal a broken bone in an animal that needs to constantly keep using that bone to survive.
Edit: Also when horses break a bone in their leg, they tend to panic and start trying to run. The flailing they do can cause very severe injury to tendons, rip muscles, tear joints, and it’s not uncommon that the bone rips through the skin, which creates a big risk of infection. So a broken leg in a horse is often much more severe and catastrophic than what we see in other animals. In some horses they flail so much from one broken leg that they break a second leg.