That's probably one of the origins for the rule. Sacred ground and easy to understand how play acting getting wounded and killed, never mind the rest of it, just doesn't sit well.
The other part, which is probably has become the larger concern, is managing the safety of particpants and the observing public. Lots of ways to hurt yourself and others.*
If there is no public, then what's the point of doing a 'demonstration'. You can't say its 'for fun' when its tax dollars on the line. Living History has more or less earned its place because it gets people interested. It works.
