I hate be a bore, but because...
a) there is neither enough rope nor lampposts in this world to satisfy "the public's sense of justice" (fuel for populism, that imaginary concept)
b) The monopoly of the legitimate use of physical force is the defining conception of the state. The way it works is that the police is empowered by the state to enforce the law, protect property, and limit civil disorder, wheras the task of the military is usually defined as defense of the state and its citizens, and the prosecution of war against another state.
... legal (and, thus, boring) solutions might be...
a) Increase police presence in places where there are needed for fining (and mayhaps arresting) adolescent idiots, rescuing absent-minded elderly tourists from being run over by marching units etc.
b) Separate the ceremonial units and the misbehaving public (e.g. with a fence)
