In an ideal (and safer) world, this would be right on the money. However, at least where I live, 4 young girls have been abducted, sexually assaulted and murdered within the past year...all within a 5 mile radius of where I live (moving is not an option at the moment, nor is my neighborhood considered particularly 'unsafe'). If anyone thinks I'm going to let my 9 and 10 year old daughters run the neighborhood unsupervised, they're smokin' something illegal. As for playing in the street, my kids get grounded for that sort of thing. Cars pay no attention to speed limits in my neighborhood and there are far safer place to play than the street (like...ummm...the back yard or the sidewalk?).
That's not to say that they don't get their share of exercise, but it certainly needs to be in a more supervised form than it was when (and where) you grew up apparently.

As for parents putting their kids on diets, these days they often don't have to. Girls as young as 8 have reported 'dieting' on their own in surveys over the past several years. Children are far more aware of body size these days and at a younger age than most people give them credit for and there certainly is no lack of information on TV and in the media about weight loss.
I'll give you an example from my own experience. When my oldest daughter was in 1st grade, she was a little chubby; enough so that the kids at school began to tease her about being 'fat'. Her pediatrician wasn't too concerned (my daughter brought up the topic during her physical) and was more or less of the opinion, "just hold her weight where it is for a while and let her height catch up". About that same time, she was diagnosed with ADD and started taking medication for it. Now, one of the side effects of this medication is loss of appetite for a few weeks until the body adjusts to it. She took advantage of that and, unknown to me until a few months later, quit eating her lunch at school for several weeks. It was only after we brought her in for a height/weight check (standard procedure for this medication) after a few months that we realized that she had dropped 15 pounds and her pediatrician freaked out. I knew she had gotten thinner and we had expected some weight loss, but not that amount. When I asked her what on earth had given her the idea to quit eating lunch, she told me one of her classmates had suggested it. I didn't put her on a diet. In fact, I was doing everything I could to encourage her to eat. She found a way to do what she wanted anyway. It took some work, but she is now back to eating normally and maintaining a healthy weight, but it just goes to show you that it's not always the parents 'putting kids on diets'.
OTOH, there's nothing wrong with limiting the junk food that kids eat. As a parent, I want my kids to be as healthy as they can be and that takes healthy food, not junk. After all...you are what you eat.