Facts:
1. Horses are inherently dangerous around people because they are subject to instinctive flight reflex behavior at any time.
2. Even the best trained police horses may suddenly decide to bolt.
3. Most police horses are not sufficiently trained to not respond to unexpected stimuli, with the resulting risk to bystanders.
Conclusion: Mounted police are for riot control, not prancing around crowds.
As for the fool who was so drunk or stupid as to contact the rear end of a horse, he got off easily. The horse could have just as easily maimed or killed the drunken fool.
If horses are spooked so easily, how can they handle a riot without freaking out let alone a busy area of people?