The problem is not dietary sugar, it is blood sugar levels, which are elevated by many things (including protein and fat), but more than anything by excess calories. The problem is not peak blood sugar levels, it is average blood sugar levels.
Edit: to quickly reply to your TLDR edit:
> Thus, protein- and fat-rich foods may induce substantial insulin secretion despite producing relatively small bloodglucose responses.
This is only true if you completely ignore everything else going on in the body. Gluconeogenesis is a thing, and just because dietary fat or protein doesn't immediately increase blood sugar levels does not mean long term they don't. This stuff can't just be looked at as "input/output" you have to take into consideration the existing state of the person before the input. /edit
You can reason about this fairly easily: take a caloric intake of 2000 calories consumed all at once vs in 10 meals over the day. The all at once crowd gets a huge insulin spike. Oh no! Fat storage, right? Sure, but what happens the rest of the day when there is no dietary input? Fat burn! The 10 meals/day crowd probably never gets as high blood sugar levels, but also has much higher throughout the day, and accesses fat stores less. But guess what? Net the body is really pretty good at smoothing this stuff out, it's sort of the entire point of fat storage.
Where this gets tricky is that high insulin can eventually lead to low blood sugar dips. People without diabetes can simply wait this out, and the body will start burning fat again and raise the blood sugar. But this also makes many people feel hungry, and so they eat more, which raises their average blood sugar levels, and the cycle continues. Some people have a hard time with this, others do not, but it's really important to understand that the insulin is causing people to consume more calories which is causing damage, not the insulin itself.