Most American dialects use constructions like that one there, and so, do many others in the rest of the English-speaking world, such as Cockney and Scots. Therefore, the outlier may be Standard English, which did not become the standard until around 300 years ago. Wikipedia has a good article on double negatives, a closely related form.
My own opinion is that the reason the redundancy survives is meter; which of the following sounds better?
- "I can get no Satisfaction"
- "I can't get no Satisfaction"
- "I cannot get any Satisfaction"
- "I can't get any Satisfaction"