A.B.
Well, technically, the kids can play in the dog park :-) Seriously, the thing is that playgrounds are a HUGE liability and are expensive to insure because they are what is referred to legally as "an attractive nuisance." Dog parks don't have playground equipment and should have much less liability and expense.
Besides that, dogs aren't allowed everywhere and do need exercise in an appropriate space. Children also require exercise, but they are allowed pretty much everywhere. There are places you can take a child for physical activity: school playgrounds, public parks, McD's, riding bike/walking on sidewalks,etc. I live in a house with a tiny yard. My neighborhood doesn't have a playground; we go to public parks, McD's or the elementay school if we want to use playground equipment.
UPDATE:
By the way, my daughter was injured by another child at an outdoor mall splashground over the summer, requiring 10 stitches to her forehead at a cost of $2,000 to my health insurance. I flat out told the splash ground's insurer that I did not consider them negligent or legally liable for the injury. Nonetheless, my own health insurance contacted me for the injury details and determined that they want the splash ground to repay them and are going after the splashground. I feel bad about that and am majorly peeved at my health insurance carrier, considering the lack of negligence on the part of the splash ground. These kind of things are why play areas get closed down or are so expensive to be insured.