I see it kind of like “light mayonnaise.” You can’t call something mayonnaise unless it contains at least 65% oil (in addition to other requirements), so if you reduce the amount of oil and/or add ingredients that are not permitted in mayonnaise (such as starch), you have to add a qualifier such as “light.” When you do this, by definition, it’s not mayonnaise; it’s “light mayonnaise,” a totally distinct item that is similar to mayonnaise in some respects but is not mayonnaise.
IMO, this is analogous to Chicago-style pizza. It’s not pizza, it’s “Chicago-style pizza.” It may be similar to pizza in some respects, but it is not pizza. Of course the FDA is not there to police the use of the word pizza like it does for mayonnaise, so you can call it whatever you like.
I’d propose a test along these lines to prove the point. Take a group of random people who have never seen or heard of “Chicago-style pizza,” and show it to them, let them taste it, and then ask them what they would call it. My guess is that few would call it “pizza.” Some may say it’s similar to pizza in some ways, but I bet few, if any, would call it straight up pizza.
I’d also bet that if you repeated the test with NY, NP, cracker, American, and maybe even Sicilian/DS, most people would call it pizza without qualification.