> And yet nearly every machine learning engineer would disagree with you, which is a given away that your argument is rooted in ideology.

That's a bold statement! Of course I know the difference, in one case you are learning from correct/wrong answers, and in the other from a probability distribution. But in both cases you are using some X to move the weights. We can get down and gritty on KL divergence vs cross-entropy, but the whole topic is about "theft", which is perhaps in the eye of the beholder.