I'm a parent of four precocious kids in a small college town in the mountains of NC.
We have taxpayer-funded public transportation here. 12 years old and up are allowed to ride the bus alone (to go to the library, etc). Would I let my 7-year old if he were allowed? No. Would I let him go with his 12-year-old brother who has a way to stay in touch with me? Probably.
I don't think the issue here is automotive safety. A fully-automated car should be safe enough for kids to ride in by themselves, or it shouldn't be on the road. I think the bigger concern is, when is it okay to let your kids out in public without supervision? 72% of the people who said flat out "no" did so because they have the impression that parents should be attached to their children at the hip, or because there was no option for, say, 15 and up. Maybe kids should be able to earn the freedom of being out without their parents with good grades above a certain age, etc. The survey sucked. There should have been an option for unlicensed adolescents but not younger children, etc. Parental consent and discretion should be part of the equation as well. We're the ones responsible for our kids, and with that responsibility should come some discretion on our part.
On a side note, I think autonomous cars will reduce the need for us to go out for non-social things. I mean, aside from losing the ability to pick the best produce, I certainly wouldn't mind telling my car to make a run to the grocery store for me. For me, shopping is just time I'd rather spend with my family.