I was recently involved in a little "edit war" on Wikipedia (now there's something of a hyperbole -- comparing a few mouse clicks to bullets and napalm) and it provided a great example of the arbitrariness of prescriptivist grammar.
"Prescriptivism" is the view that there is such a thing as objectively "correct" language, and the imposition of rules on everyone's language.
It is the prescriptivists that teach us that you use "may I...?" to ask for permission to do something when in natural speech we practically always use "can I...?". The dangerous thing about prescriptivism is that we believe the myth and spread it, even though we don't actually do it ourselves. So a native speaker will often "correct" a learner who uses perfectly normal, natural English. This is a Very Bad Thing, as it makes it much, much harder for the learner.
Anyway, the prescriptivist will tell us that double-negatives are very, very wrong. Well, there was a time when they weren't, and English operated much like the rest of Western Europe, not doing nothing to nobody. The prescriptivists got their way, though, and eventually they managed to drive the English double-negative to extinction.
For some reason, many of the same prescriptivists who insist that "a double negative is a positive" (and there ain't never been no truth to none of that) will also insist that not ... nor is "more correct" than not ... or, and likewise neither ... nor over neither ... or.
Why have people in general stopped using nor? There's a very simple explanation: we don't think in double-negatives any more -- the prescriptivists taught us not to. Nor only ever existed as the second of a double negative.
We can split most negative pairs and have two valid modern English sentences:
I haven't never been there -> I haven't ever been there / I have never been there
I haven't done nothing -> I haven't done anything / I have done nothing
But look what happens when we try that with nor.
I had neither one nor the other -> I had neither one or the other / *
Keeping only one negative in the sentence produces two options: keeping the first negative (not or neither) gives a clear and comprehensible sentence; keeping the second negative results in a sentence which is unclear and difficult to comprehend. But we had to lose one, because our model of English rejects the double negative. Hence we lost nor.
Arguing against "I ain't done nothing" while simultaneously arguing for "neither... nor" is likely telling everyone to take up a vegetarian diet, but saying that bacon isn't meat....