With all other words relating to absence of negation English uses the "binary toggle" interpretation (which is only binary as long as the described concept is binary). For example "Nobody is never not doing it" is equivalent to "nobody is at least sometimes doing it" is equivalent to "everybody never does it".

Two negations on different parts of the sentence also don't reinforce each other: "not everyone is not doing it" if equivalent to "some people are doing it".

To me treating double negative as reinforcement of the negation is a weird, unintuitive corner case that doesn't fit in the broader framework of the English language.