I think the main concern should be the kid's safety. Would you, as a mother/father be rhappy knowing that your son/daughter could be sitting next to any nutter who wants to move next to them?
Of course FA have to look after them, but it is not always possible to check as the situation would require. In a company I used to work for, a male pax moved next two UM and did some very explicit things before he was discovered by a FA.
I sure wouldn't let my son/daughter fly alone knowing that the company hasn't the policy of not allowing stranger pax next to him/her.
And knowing that lots of parents harm their children is not a good argument to let your child alone among strangers.