This is because horses have barely any blood or muscles in their legs. its mostly skin, bone, and tendon.
Combined with the bones being huge in the absolute (lots of resources to fix), but light and tiny in comparison to the rest of the body (fragile yet must bear enormous PSI).
Then factor an absolute biological NEED to stay upright almost all the time (prolonged lying down will cause horrible damage and lead to death) and being too heavy to reliably do so on 3 legs... it means they simply do not heal from a broken bone. Cherry on top, the horse's instincts which will result in it rebreaking constantly as it tries to heal.
There have been many attempts. you can pour in tens of millions of dollars into a single horse, with massive amount of equipment and human labor and knowledge, invested into trying to heal a broken leg for a horse. and it just failed and the horse eventually died in horrific agony.
(there are exceptions depending on the exact nature of the injury. some injuries can heal)
However. equestrian ponies are very light, very durable, have much better ratio of legbone size to body weight, and are perfectly capable of lying down on their back to rest, and are sapient enough to understand and suppress their instincts to ensure proper healing.
All in all, they should be capable of healing a broken bone just fine
To quote the great sources:
But jokes aside - you are very on-point. Though I think nowadays its not THAT big of an issue, just an incredible lot of hassle. I've heard there are methods - the horse should have its leg fixed, should be placed in suspended harness in its pen, being daily cared, massaged, fed proper diet, vet checking on it frequently, it should be given some short exercises to give her body a breather, etc. I don't think its a question of tens of millions, but that would be very expensive and very hard, and would require a lot of time.
As for the ponies of Equestria - they can actually stand on two legs. Not their preferred way, but the fact they can do it speaks volumes about how strong they are to their body mass. But they are also kinda magical, all of them, so its not a fair comparison.
But the point (of dragon's cock) was (sadly not) on centaurs (centaur fucking when?!). The problem is - where horse has its head, they have an entire human upper body. They are noticeably heavier than a horse of comparable size, and to distribute the weight evenly, would probably have to grow some extra thicc bums. So, for them the problem of broken leg is even more dire, hence my comment.
How the centaur is supposed to walk on three legs? And perform as chief? Not fall behind everyone, retain enough prowess to deal with upstarts, etc?
There is so much mystery hidden there! So much goddamn mystery!