That's super snowflakey, I think. I'm not sure if there are different regional terms for "dog park," but I'm assuming that in this case, we're talking about a smaller, probably fenced, area that is dedicated for off-leash running about. If that's the case, then it's mostly for dogs, and humans should stay on the sidelines to let the puppies frolic as they will.
However, I think it's important for any pet owner to have verbal control over their pooch, even in areas where the dog is allowed to be (or encouraged to be) off-leash. It's simply a matter of respect for other people and other dogs. A kid getting knocked over because he was tearing around and collided with a dog is mostly at fault (okay, his parents are). However, a kid standing off to the side watching isn't really to blame if a big dog jumps up to say howdy. Should people bring their toddlers into the dog park for the heck of it? No. But I'm not sure I think families with children should be banned from bringing their own dogs into the dog park if the kids know and respect the rules.