No, that is definitely just an urban legend. First, the law would depend on the state, and second, most states don’t have restrictions for kids once they are 7-8 years old, which I consider way too young to be by themselves but I wouldn’t get arrested over it.
> Phillips, Debra Harrell’s attorney, confirmed there is no age at which a child can be left on his or her own specified in South Carolina law. The challenge for the prosecutor will be to prove that this child’s needs and care were not adequately arranged before she was left at the park, he said.
There is no law against it (in South Carolina at least). The law they are using for the charge is reckless endangerment. And usually at the end of it, prosecutors drop all charges due to lack of evidence.
All these things make public playgrounds just extremely inconvenient. It's such a treacherous hazard I can't in good conscious consider it as anything close to a substitute.