The problem with those views is that parents are voters and you will never get them to give up their rights.

Not sure exactly which views you mean. But people vote to give up rights more often than you'd think. Sometimes this is good, sometimes not. Two U.S. examples that come to mind are the 14th Amendment, and the USA PATRIOT act.

Also running away is a horrible idea in most cases as it puts a child in a more harmful environment than they once were.

Of course. It's a very drastic step for a young person to take. But if they do, I think it's time to consider that there might be something drastically wrong. For instance I assume you are a good parent, so I would imagine none of you your children have ever run away. (I'm not talking about huffing off and hiding in the park for an hour.) But I would also note that the fact runaways can except no help from the authorities makes it even more dangerous.

I would think an arrangement that only includes government if needed would be the best arrangement for all. I personally don't want my decision scrutinized by the government it should be a family choice.

Agreed. Perhaps the government should even be less involved than it is currently. Child protective services is a necessary evil, but sometimes I think they do more evil than necessary. My own family had a few run-ins with them. These were more annoying than harmful, but I've known people who had much worse experiences. I envision the State's ideal role in this as an arbitor for serious disagreements, not a micromanaging buttinski.