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, but still, carmine is hardly “insect part” by the time the processes used to extract the compound are complete. It’s almost as if water that once used to be a part of the body of a pig, can no more be “kosher” even though it is merely a chemical compound, identical in all objective respects to any other water. Like dust mites, it cannot be avoided (I have heard it said a glass of water will have every molecule in it spread evenly all over the planet in about 12 years). Dust mites can easily surpass the arbitrarily-drawn fraction of a part in sixty, in certain food ingredients. Couple that with other insects, it will be even more unavoidable.