When dieting long-term the body becomes more efficient with the calories coming in. Metabolism slows, more aspects are taken over by fat-burning. Fat contains twice the energy per gram as carbs or protein. I think a lot of the stall business is gluconeogenesis. Excess protein turning into sugar and ultimately fat. There are guidelines to show how much protein the body needs each day. But I think we all fall into a bell curve. At either end the protein could cause weight gain or loss while for middle majority it causes a stall. Just a guess.

I agree with your point:

"...a weight loss stall means CI=CO by definition"