I think it was convenience and her generation always having to be the one to cook for the family.
You are mostly correct, in terms of effectiveness.
Also good are exercise (building lean muscle mass), reducing carbs (a la keto, paleo), and intermittent fasting (keto).
There are other health benefits to cutting carbs, especially HFCS: reducing obesity, heart disease, diabetes.
Just think of the strategies as complimentary. And do what works for your body (eg consuming too much potassium can worsen some heart conditions).
Modern nutritional science is also showing that the way food is digested and metabolized in the body is strongly influenced by a complex hormonal interchange -- and whether organs like the liver or the gut are predominantly responsible for macronutrient metabolism has a significant effect on, for lack of a better word, "effective calorie counts" in foods. The macronutrient composition of what we eat clearly affects our hormonal reaction, which clearly affects feelings of hunger and satiety. To ignore these feedback loops in favor of strict energy-deficit reductionism is a bit like saying that anyone not programming in binary is wasting his or her time.
Sometimes science literate ppl think these ketoers just don't understand the 2nd law of thermodynamics, but that's not the point. Its true that the 2nd law determines weight loss, but changing your hormonal response is how you really achieve a healthy lifestyle.
Further, many people would rather not have to track their calories everyday for the rest of their lives in order to maintain a healthy diet. They'd rather condition their body to prefer healthy foods, and to prefer healthy quantities of healthy foods. To do that you have to look at the source of the calories, not just the amount of calories.
It's not strictly speaking a rebuttal, but it illustrates a point quite clearly, fat is not the culprit.
Italian people are among the least overweight people in the OECD countries, and have a heavily carb based diet. (I think the same applies to Japanese and Korean, but I think there could be a prevalent genetic factor there.)
That's not to say that fat makes you obese, just that carbs, per se, don't. Eating too much does.
When left to her own devices, she will consistently confuse and/or conflate carbs and fats. I think this is because she's from a generation that totally bought into the war on fat, and raised us accordingly. Fat is so evil in her mind that there is a subconscious revulsion to it.
I'm not sure older generations' assembly-level worldviews can be reprogrammed at this point. Carbs will be ubiquitous until younger folks become the predominant consumer power in the economy -- or unless someone actually influences the Boomers somehow, e.g., convinces Dr. Phil or Ellen DeGeneres or Gwyneth Paltrow or Matt Lauer or whoever to come out strongly against carbs.