Isn't this why ketogenic diets also limit protein? I think you're right that if someone is eating a low-carb diet but also eating excessive protein, they wouldn't be adhering to an insulin-based theory.
Ketogenic diets seem best understood as diets that put fat intake as high as possible. Some protein intake is necessary, to obtain essential amino acids, but ideally not more than that. Carb intake can almost entirely be eliminated, because there are no essential carbs, and plant consumption can focus on low-carb plants (e.g. nuts, leafy greens).
I don't mean to endorse ketogenic diets, since I don't know whether they work. But they're at least internally consistent provided protein intake is also limited.
The keto diets most people follow are loaded with animal proteins and fats, although they don't have to be that way. There are some benefits to a healthy keto diet but there are also some serious risks, particularly in the longer term.
Ketogenic diets seem best understood as diets that put fat intake as high as possible. Some protein intake is necessary, to obtain essential amino acids, but ideally not more than that. Carb intake can almost entirely be eliminated, because there are no essential carbs, and plant consumption can focus on low-carb plants (e.g. nuts, leafy greens).
I don't mean to endorse ketogenic diets, since I don't know whether they work. But they're at least internally consistent provided protein intake is also limited.