Actually, I (and other proponents of “carb control” diets) recommend a fairly low intake of carbs on a “base” diet (about 25% carbs, 50% fat), but that during fat loss, calories should be removed from the fat intake since the body is basically going to be supplementing fat from stored body fat. The base diet is what you would eat if you weren’t “training” though it would account for your normal daily activity. And during a weight gaining period, or a period where training (which should be most of the time) added calories should come mostly from added carbs.
Let’s say that a base diet for someone not training then is
600 cals from carbs (150 grams)
600 cals from protein (150 grams)
1200 cals from fat
2400 cals total.
That is basically the maximum fat intake that you would ever use.
If you want to cut 600 cals a day, you would go to:
600 cals carb
600 cals protein
600 cals fat (the other 600 coming from stored fat).
If you want to add in an hour of resistance training you would add maybe 400 cals but mostly carb, such as 300 carb, 100 protein.
That would bring the “base” up to
900 carb
700 protein
1200 fat.
IF you want to do both you would be at
900 carb
700 protein
600 fat
So start with a 25/25/50% split using your resting or non-training caloric expenditure and then a) reduce fat intake for fat loss; b) add “periworkout” nutrition (carbs and some protein) for training.
I think that the reason that a lot of people recommend cutting carbs to lose weight is because the starting point involves people who are way above 150 grams of carbs or 25% while sedentary. The other reason is that cutting carbs will lower scale weight faster because of a reduction in water.
Reducing fat will improve insulin sensitivity as much as or BETTER that reducing carbs. People on high fat diets secrete far more insulin per gram of carbs ingested than people on low fat diets to the point where total insulin needs are virtually the same. If you burn 2400 calories a day, and you eat 1800, you will improve insulin sensitivity just as much if you cut the 600 from carbs or from fat. Cutting carbs may actually reduce low blood sugar by preventing rebound hypoglycemia that can lead to hunger.
OK the one problem can be that lower GI carbs often are more inflammatory or allergenic (such as beans or wheat versus white rice) but the key is to avoid large amounts of white rice etc. all at once and removed from periods of activity.