Hot take

Low-carb does not improve blood glucose by reducing glucose intake or decreasing insulin response but *entirely* by causing a reduction in calorie intake by other mechanisms. What’s more, the major proponents of low-carb diets for diabetes don’t know this. Incredible!
Explanation: no study of carbohydrate-restricted diets matched for calories, protein, etc. has ever shown an improvement in average blood glucose or HbA1c, and I think there are many indications that no study ever will. Though we need to directly test this!
Caveats

Caveat 1:

PUFAs reduce liver fat compared to other macronutrients, so a low-carb diet high in PUFAs should improve glycemia compared to baseline when matched in calories, protein, etc. (PUFAs = polyunsaturated fatty acids, high in nuts and seeds; eat nuts and seeds!)
This is because, according to the current understanding of the cause of hyperglycemia, liver fat is closely related to glycemic control; reduce liver fat, reduce blood sugar.
Importantly, saturated fat is terrible for liver fat, so a high-SFA low-carb diet (which is standard fare from low-carb gurus) would be suboptimal for improving glycemia. (Hmm, when we switch the focus from insulin mythology to following the data, we can serve patients better...)
Caveat to caveat 1:

I am not sure it is known whether PUFAs (say, in the form of nuts or seeds) or unrefined carbohydrates such as legumes would perform better for reducing liver fat on an isocaloric, same-protein, etc. basis.
It may be that PUFAs are better than SFAs and refined carbohydrates but not much better than highly unrefined carbohydrates. If anyone knows, I would love to know.
In any case, it may be the case that one would see an increase in liver fat if transitioning whole foods plant-based diet to a low-carbohydrate diet high in saturated fats!
This is remarkable to think about, since while low-carb gurus claim their diet to be optimal, it actually may be worse for diabetes remission than some other diets like WFPB (assuming one matched the WFPB for protein, etc., which, granted, may not be common in the real world).
Caveat 2:

Protein does an amazingly good job of reducing liver fat. A low-carb diet with increased protein would be expected to improve glycemia, even when weight remains stable and fiber, etc. are matched.
A great protein source that covers both caveats 1 and 2? Fish! Try sardines. Importantly, fatty fish are among the only animal foods that show a consistent signal for improved longevity in the observational literature.
Caveat 3:

Fiber would also be expected to improve glycemia. In fact, while it is sometimes claimed that "fructose" increases liver fat, this has never been demonstrated in an adequately controlled trial;
It *has* been shown that free sugars (including free glucose and not specifically fructose) increase liver fat. Fiber, presumably, is the factor that prevents this from happening.
Caveat 4:

Free sugars have been shown to increase liver fat, and fructose is a free sugar. We would therefore expect that replacing a diet high with one low in table sugar (and low in SFA) to cause lower liver fat, all else equal.
What does this leave us with?
A low-carbohydrate diet will reduce liver fat if, compared to baseline, it is:

1. Restricted in calories, or;
2. Higher in PUFAs/MUFAs (many plants) and lower in SFAs (many animals), or;
3. Lower in table sugar or HFCS, or;
4. Higher in fiber, or;
4. Higher in protein.
A low-carbohydrate diet will be LESS optimal in reducing liver fat if, compared to baseline, it is:

1. Higher in calories;
2. Higher in animal fat and lower in plant fats;
3. Lower in fiber;
4. Lower in protein.
Regardless, it is most likely the case that weight loss reigns king, but there are other things one can do to optimize a low-carbohydrate diet.
It is likely the case that many low-carbohydrate diets can, compared to many baseline diets, induce weight loss even while getting much of the above wrong, thus producing a reduction in liver fat, improvement in glycemia, etc.
This happens independent of mechanisms related to insulin (which probably isn't per se very important for fat loss) but for reasons related to satiety signals sent to the brain, which, for reasons still poorly understood, low-carbohydrate diets seem to be effective for.
(Though not necessarily optimally effective for weight loss either. See @KevinH_PhD's recent study: https://twitter.com/KevinH_PhD/status/1258102121246806017. But we still need more data!)
Low-carbohydrate diets are not a panacea for glycemia by any means, and there is no good evidence that simply replacing carbohydrate, especially unrefined carbohydrate, by fat would help improve blood sugar.
How much glucose one is taking in, nor one's insulin levels, just do not appear to be the main issues.

Rather, how blood glucose output from the liver is regulated seems to be more important, and this is related to liver fat.
In fact, replacing unrefined carbohydrate by saturated fat would be expected to worsen liver fat and might even worsen average blood glucose! Although I do not know whether the final inference has been directly demonstrated yet.
Most low-carb gurus do not seem to care about these nuances, though there is a rich literature documenting them. It is remarkable to think about, since they often appeal to "rigorous science" or the "latest science", which they don't actually care about.

It boggles the mind.
I will try to get together a blog post detailing these points and providing references sometime this week. I just need to collate a bunch of tweets...
A common objection is that eating carbohydrate causes a greater post-feeding spike in blood glucose than eating fat. True, carbohydrate feeding causes increase glucose variability, which may independently be a problem.

But does carbohydrate cause higher AVERAGE blood glucose?
There are three reasons why it might not:

1. Carbs might produce a larger peak in post-feeding BG, but fats might widen the overall spike;
2. Higher post-feeding BG from carbs vs. fats might have a relatively modest role in determining average BG;
3. Fasting BG could be lower in those who consume more carbs vs. less (though I don't think this has ever been shown).

Regardless, the point is: where is the evidence for an average blood glucose improvement on high-fat vs. high-carb diet, if matched for calories, protein, etc.?
I have never been able to find this evidence; I have only found much evidence that the more matched the diets become for the relevant factors, the smaller the difference in HbA1c (a surrogate for average blood glucose) between diets...
So we follow data rather than theories.

And a lower post-feeding (postprandial) blood glucose peak will not necessarily translate into lower average blood glucose values.

If it did, this would need to be demonstrated by actual DATA.
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