That attitude is rather a shame, I think. How are we expected to raise a generation of functioning, independent adults if the default expectation is that kids are constantly chaperoned? The societal dangers are familiar to anyone who's tried to deal with the average intern.
Unaccompanied minors on US airlines are very common. The service works well, most of the time, but when it fails the result is always a lost, scared child and some very angry parents. Headlines inevitably follow. In this case, United's callous treatment is utterly deplorable. Please understand that it's the airline that's at fault here, not the parents for availing themselves of a tried and tested service.
Children are humans, therefore highly adaptable and a lot smarter than anyone thinks. Lone children as young as six are frequently put in charge of an entire family's herd of goats in Kenya; now, granted, there aren't the same dangers from traffic or population density that you'd find in a city, but the herd represents the majority of the family's wealth and it's therefore an awesome responsibility. Imagine herding your parent's entire net worth at that age! Kids that young take the bus - the regular commuter service - to school alone in the UK all the time. I see young kids in NYC taking the subway alone every day. Very, very rarely is there a problem; certainly no more so than a mother doing the school run rolling her SUV.