It would if it were the whole story, but it’s not. It is absolutely true that gluconeogenesis is a demand driven proccess and that we needn’t worry about too much protein driving blood sugars to insane levels. However, what’s left out is that excess proteins are converted into energy in our bodies via many, many different pathways. Mostly the excess amino acids are deanimated and their carbon skeleton is fed directly into the Krebs cycle to produce ATP.
What’s important about this, and which I see ignored a lot on this forum, is that excess proteins are always used preferentially over fats since there is almost no storage for them in our bodies, it’s even used preferencially over carbohydrates. Thus, while our bodies are dealing with this excess it is not burning fat.
I’ve noticed that people here respect Amy Berger and point to her blog about protein and gluconeogenesis a fair bit, but somehow don’t see that in that blog she also says all of the above.
People like Phinney and Fung understand this biology and thus are very careful in describing this diet as moderate protein. You don’t want to eat protein in much greater excess than you need for upkeep, maintenance, and whatever growth you may be after via exercise.