I wonder what their reasoning is behind banning non-powered bikes? It's got very steep hills, so there's a good chance that bicycles wouldn't be very practical, but seems strange to ban them.
Bikes, even muscular ones, can be annoying to pedestrians on thin hiking paths. My take is that even if they allow one/a few/a capped number, then it's out of the bottle, and people will try to game the system one way or another