You are right, to think the body has an on-off switch like that doesn’t really make much sense. That sure would be a crappy, non-adaptive, system. Whatever small rise will most likely be transient, and not really matter in the end. From what I’ve seen from prominent scientists and clinicians in the field and related fields (like longevity), that’s pretty much what they think, even if there is no clear evidence on how much of an effect it would have (we barely are only scraping the surface on what fasting actually does, scientifically speaking, anyway). I think I’ve seen some stuff from keto people measuring blood glucose after like some coffee + creamer, and it does in fact go down back to baseline again very quickly.
Some scientific evidence would be, for instance, Valter Longo’s research where they use a fasting mimicking diet, i.e. people eat, but just way less - about 700 kcal a day, low carb and low protein. Plenty of other research into VLCD, or very low calorie diets, where they had great results on for instance diabetes (which, to be fair, could have just been from the weight loss). The most important thing is what you can stick to, anyway, and not what is 1% better or perfectly optimal.