Insulin is not required to metabolize fat. You make insulin when you eat glucose, and alanine in the presence of leucine. You also make insulin when your stomach stretches. So if you eat a lot of fat you might make a little, but not because of the fat you could eat gravel and it would have the same effect.
But what insulin does do in a healthy person is it tells fat cells to hold on to their energy, because it is primarily an energy signal that glucose (or the amino acid alanine) is present.
In a metabolically damaged person that inhibition is blocked and the fat cells are continually releasing floods of energy into the blood. The problem is that a metabolically deranged person also could be making like 10x the insulin trying to shut off the spigot … and it won’t turn off. We make way too much insulin even when there is no incoming glucose.
The other thing that insulin does is it shuts off clean high volume processing of fat in cells into energy. So in a deranged person we make lots of insulin (because tissue all over the body is becoming resistant to it), we can’t shut off the spigot of our fat cells releasing a flood of energy into the body, and cells only use fat slowly (and produce a lot of H2O2 in the peroxisome in the process). Meanwhile all the fat is pushed into every cell in the body which causes cells in the pancreas and muscles to become more insulin resistant.
That’s what type 2 diabetes is. Too much fat being released into circulation from insulin resistant fat cells, and not enough being drawn down by insulin inhibited mitochondria.
The reason a diet low in insulin stimulants (cutting carbs and protein to a minimum) works is because it lowers insulin low enough to enable cells to burn fat (and the fat adaptation improves the speed you can get fat into cells, and increases the enzymes in the cells for dealing with fat).
The reason I believe that people who are hyperinsulinaemic stall at a higher point is that their fat cells slowly heal now they are no longer full to bursting, and they become more sensitive to insulin and stop releasing fat into circulation - which is what healthy fat cells are supposed to do when insulin is high. And because their basal insulin is still above 13 mU/l the stop releasing fat into circulation.
That’s why the way to move past the stall is really to use strategies to reduce basal insulin … like IF, or EF, or muscle building and glycogen depletion (HIIT).