A well thought out Ask, Dr. Mark. A lot of people need to try to keep in mind the viewpoint of parents with new things like this. It's hard to imagine that people would be so against something so innocuous, but they are.
I was fortunate enough that at least one of my parents was a gamer as well. Mind you, he only played the earliest consoles and early PC games (he still plays some of them, but he's not the best), but the fact that he found them a good use of time means that he saw they were an okay use of time for me.
I also know what you mean by parents limiting time, or attempting to do so. During summers, it was impossible for my parents to limit my time. I had grown out of daycare and we couldn't afford a babysitter. They were both at work, so I spent most of my time playing with LEGOs, reading, playing SEGA or PC, or visiting a friend.
Eventually, about the time where internet started becoming more popular in homes (woo, dial-up!), my parents tried limiting my time on a computer. This worked to a degree, as they had to let me online. Eventually though, the computer was online constantly, and it was more difficult to limit me since they weren't around.
It eventually turned into no time limit, as there was no time for them to watch me.
Maybe once we have cheap, efficient, and safe NannyBots, then children can be more effectively limited.