I also used to find this disturbing, but
the way I have explained this to myself is --
Insignificant < 25%
Not insignificant 25-50%
Not significant 50-75%
Significant > 75%
Of course for each individual situation the numbers vary, and I use them simply to demonstrate that it's a matter of degrees, and not as binary as you may expect a typical "not" to be.
It is the only double negative I have come to find useful.
Probably, although sometimes these become terms of art, i.e. words or phrases with quite a specific meaning in a particular field. (Think of the people who hear 'significant' as '< 5% under null hypothesis', ironically not what Fisher intended)
It's the rhetorical figure called "litotes" and has been common in many languages now and throughout linguistic history. https://en.wikipedia.org/wiki/Litotes
I am aware. I was not saying that this is a characteristic of the English language, merely that it is more commonly use in the English spoken in England than in the United States, for example.
The "not un" has a long history of debate amongst stylists. I believe it's easily overused because it has certain air of erudition about it. However, sometimes "not un" is straightforward and clearer than the alternatives. In this context... well.. science journals have their own English journalese that lives outside general usage.
The double negative has its use beyond language sophistication. It can serve to more specifically mark a neutral stance in a vocabulary that may seem to only offer a dichotomy. e.g. what I have available is I like her and I don't like her, but what I mean to say is I don't dislike her.
That example sentence is a perfect usage of an English double negative, the only thing missing is the emphasis which should be on "dis" - if spoken without the emphasis it becomes simply a statement on not disliking someone without the hint that one also definitely doesn't _like_ the person.
