Inevitably, this will lead to allowing bull fighting,cock fighting and camel fighting
I disagree. The horses are not the targets.
That would be good.
Bull fighting and cock fighting already have huge fan bases, much more so than most Olympic sports. Cock fighting may be a bit of the problem as none of the participants are actually human, but that may be a quibble.
I’m not sure about camel fighting, that seems a bit of a novelty, but I’d be fine with giving it a try.