Technically, nothing could be labeled "kosher" if insect parts cannot be used because things like dust mites are guaranteed to be present in parts if not whole, in all processed and natural foods.
Logically, there's no reason to avoid the "kosher" label for using carmine (a chemical prepared from so many processes to extract a coloured acid from insects, it's practically merely a chemical compound), if other foods can be allowed a "kosher" label while containing dust mites.
Ah, but you're overlooking the fact that rabbinic law (which defines kosher) regards the unintentional presence of non-kosher ingredients in sufficiently small amounts (if I recall up to 1 part in 60) as inconsequential -- I forget the Hebrew term (which I only ever knew because Norman Podhoretz cited this rabbinic regulation by way of analogy in defending Patrick Buchanan against accusations of antisemitism). No one puts dust mites in their food on purpose and they don't constitute very much of it, but dyes are put in food intentionally, and thus would need to be kosher for the food to be kosher.
Yes, I’m given to understand that the Rabbis draw the line at anything too small to see with the unaided eye.
NYC tap water needs to be filtered to remove just barely visible copeopods to be considered Kosher.
It’s further complicated by the fact that not all insects are treif...