Not exclusively, of course, but the degree of processing of food greatly influences our body’s insulin response, which can over time have huge impacts on health (leading to fatty liver disease / metabolic syndrome / obesity / diabetes). This is why, for instance, fruit juice is so much worse for us than the whole fruit — most of the fiber is removed which would otherwise slow down digestion and temper insulin response. For more info I’d highly recommend Jason Fung’s Obesity Code book — he’s a nephrologist specializing in diabetes treatment.
Some kinds of processing increase insulin impact, others don't. If your goal is controlling sugars, a diet premised solely on minimizing processing isn't a great strategy; "processing" isn't the high-order bit of that problem.
Theoretically, you are right, of course. In practice though, to apply this, you would need to know how the processing exactly works, and how the body responds to that processing. Given that you can not really determine this easily, it is in practice just simpler to stick to unprocessed foods as much as possible, and just apply the sugar limit to those.
I don't think this makes a lot of sense. Cheese is cooked, fermented, emulsified, and aged. It has a lower glycemic impact than milk, its primary unprocessed input.
Mostly, I think the "processed" vs. "unprocessed" debate is an appeal to tradition, not science; if it's a kind of processing we were doing 200 years ago, it's OK; otherwise, it's unhealthful.
I would say that Cheese, at least its classic variants, fall exactly under the category where you have fairly good knowledge of the nature of its processing and its effects on the body. I'd say your example supports my argument.
