Regina, Saskatchewan; Canada
A similar thing may be seen with the word mouse that Old English spelt as mus. Mouse is also spelt as mus in Old Norse, Latin, and Sanskrit. These words are just cognates though, not loanwords. "Ne" was the regular word for "not" and "nor" since the first traces of English, and could be used with or without other auxiliary negatives in the sentence. Notice how all the negations mentioned above are from words that begin with a vowel, the letter w, or the letter h. When ne preceded very common words beginning with those letters such as was, will, had, ever, one the ne became contracted with the word making nas, nill, nad, never, none etc. Almost all negatives in English come from such contractions.
I don't think it is bad grammar at all. It is just unfamiliar good grammar. If no one ends up reviving some of these negations, then at least they may still learn what they are finding in such passages as those below from Chaucer's "The Knight's Tale":
"I nam but deed, ther nis no remedye."
"I not which hath the wofullere mester"
"His spirit chaunged hous and wente ther,
As I cam nevere, I kan nat tellen wher.
Therfore I stynte, I nam no divinistre,
Of soules fynde I nat in this registre,
Ne me ne list thilke opinions to telle
Of hem, though that they writen wher they dwelle"
"This world nis but a thurghfare ful of wo,
And we ben pilgrimes, passinge to and fro"
You know Fowler on split infinitives; and, as I recall, disagree?
I don't have a problem with a few split infinitives, just as I don't have a problem with a few spelling mistakes. No one is perfect. But just like spelling mistakes, I think we should try to avoid them, rather than pretend they are not mistakes.