I think the younglings and elderly are there for the upset cyclists to take out their frustrations at not being able to ride their bikes, not for just anyone to come by and abuse...
It is a silly rule to be fair. Sharing the sidewalk with pedestrians is perfectly fine anywhere else but the moment it is in the park it becomes dangerous?
In my experience this kind of restriction tends to be in areas with narrow walking paths that have short turns and are actually terrible for riding a bike even if there weren't other people around.