Completely agree with your logic. Most native speakers indeed do not use commas on a regular basis, which does not make the commas optional if you want your sentence flow to be smooth and readable.
Whether you write no thank you without a comma or no, thank you with it, it has the same exact meaning. it's just one is more clear syntax that you understand that comma should be after the no. No thanks without it, doesn't mean you remind them you haven't been thanked, it just means 'no thanks' as a whole sentence. If you were Questioning why you were not thanked, you would need more context in