The core belief behind South Park is that children aren't born pure and righteous but then twisted by society. Rather, it is the job of the parents and society to mold them into good people. Kid's aren't the example for society to follow, rather they are the ones for which parents and society should be setting the example for them to follow.
Left to themselves or the twisted "village" most kids are raised in today, they become little Cartmens. The show is meant as a "scared straight" for parents rather than an influence for kids.
The kid with the most normal family is the most normal kid. The kid with the single parent whore mother is pure evil, the kid with parents on welfare gets killed every episode, and the kid whose parents are too strict and controlling is neurotic.
They don't need to be vulgar to be funny, they are vulgar for the purpose of demonstration: let the village raise your kids and this is the result. South Park isn't saying "let your kids do this", it's saying that if you don't do your job as parents this is what they'll do.
Nicely put.
Children are by nature lying little troublemakers.