I know what you are getting at, and the problem is that you assume that there must be a certain innate logic to language, much as the original English grammarians did.
Nothing "English" about it. All of these ideas are washed-up Latin has-beens that migrated to other languages.
Although the Sanskrit grammarians developped many very parallel ideas.
Nominally. Really, of course, it's because a double negative wasn't done in Classical Latin (although I'm not sure about
their reasons). The purging of double negatives from the Germanic languages was part of the campaign to "civilise" them by making them more similar to Latin.
It's not, actually - for the received French grammar isn't an example of a double negative at all, though it looks like one to the casual observer. It's just a negative formation built of two words - ne pas "no step" ie not, ne rien "no thing", ne jamais "no ever" (in these latter two the positive sense is extinct, but that's the etymology), ne que "no but" ie except, ne plus "no more". If these are double negatives then so is English "nothing". They work completely unlike actual double negatives, and "ne" can never stand alone.
However, in the spoken language the ne can indeed be dropped - just a common case of slurred speech. It's a small particle and the meaning of the sentence, except for a few ne...que formations, is immediately obvious without it* - so
in a non-historical sense the other word is, indeed, a negative. But you can never learn anything really worthwhile in linguistics without at least a sideglance at historical linguistics.
And here we get to the really interesting point: Because spoken French does indeed have what, viewed ahistorically, are double negatives - real ones this time. In written French these constructions are of course sort-of triple negatives: (ne) plus rien, (ne) plus jamais "not anymore", that sort of thing.
*Of course, this is actually what happened with "I could care less", too.