I have witnessed parent´s negligence many times (Take a look at the landcrusier next to you and you are likely to see small kids bouncing up and down)

Yes, it is parent´s responsability. Unfortunately, not every parent is a responsible parent and the children shouldn´t pay with their lifes for their parent´s carelessness. I believe the municipality should take charge as well by ensuring that public places are as safe as possible and fine parents when appropiate.