No dog parks in my area, but if there were I would probably feel similar. Of course well-behaved children who are taught manners, i.e. asking permission to pet the dog first, not screaming and yelling and running wildly around the dogs, etc, I would have no problem with. However, there's no way to keep those types in and the other types out really. So I would think there should be a section at least where kids under a certain age were not allowed at all, for dogs who aren't used to small children to go.

As far as expecting no dogs to not chase a running child, I think that's unreasonable at a dog park. There are probably young pups there to get socialized as well as older dogs to run and play. If someone runs it's a natural instinct to chase after it. Of course if I was in an off-leash area that is not designated specifically for dogs, then in that case they should be trained and expected not to chase people biking, running, etc.

I gather the park is totally a place to let the dogs do what dogs do, to play and just be dogs. It sounds like a very nice socialization tool. If I had a young pup I would take him or her purely for that aspect, and gradually work up to better manners and obedience while there.

Just my thoughts.