Where's the evidence? I linked to a study, one that isn't confounded by weight-loss (unlike the studies you people like to cite) demonstrating that as the fat (especially saturated fat) content of the diet increased to an absurd degree (55%!), insulin sensitivity tanked. Why would insulin sensitivity, when measured by an Oral Glucose Tolerance Test, suddenly improve if you restricted carbohydrate even further? Yeah, at some point your intake will be so low that you can "game" an HbA1c or fasting BG test, but underlying insulin sensitivity will be trash (which an OGTT would show), unless maybe you lose enough bodyfat to offset it.
Why do so many people on keto develop "physiological insulin resistance?" Why does all of the epidemiological evidence show strong inverse correlations between low-fat carbohydrate consumption (like whole grains and fruits) and T2DM, but the reverse for high-fat "carbs" like cookies or pizza?
The most reasonable interpretation of the data right now is that high-fat diets make you less insulin sensitive.