Population Control and Protein Deficiencies

I have decided to dedicate my post to two different issues I had while reading Chapter Four.
One of them was the issue of sacrifices being a means of population control. According to the book, "S.F. Cook...argued that the demographic impact of the warfare/sacrifice complex would have helped to alleviate population pressure in Late Postclassic Central Mexico..." The author relatively quickly refutes this  as a logical answer for population control. He mentions that the wars raged in the name of expansion used the captives as their means of sacrificial victims. Therefore, leaving the more densly populated areas, such as Tenochtitlan, still very croweded. However, I can see where Cook may have been going with this. Is it possible that because of all of the able-bodied men that were dying everyday in the fighting have been a means of population control along with the sacrifices? Also, I believe that we learned that people were also sacrificed for doing good deeds. Has any evidence or theories arisen from great warriors  being sacrificed because of something heroic they did in battle?

Secondly, I was extremely confused on the section that was dedicated to protein deficiencies. I do not think the Inca's knew about protein, but I may be very wrong. I believe they would have been more devastated from a shortage in maize, beans, and squash simply because it was a staple food, what they ate all the time and perhaps enjoyed the most. I don't think that the amount of protein had anything to do with it. We learned early on that cannibalism may have been a practice right alongside that of sacrifice. Sacrifical victims were reverred in a higher sense because, in a sense, they were going to meet the Gods and be given up for them; a gift. Therefore, eating their flesh may have been just a ceremonial event rather than a means of gaining protein when there was a shortage. Is there anyway someone would be able to explain this section to me a little better? I reread it a few times and I may just be lost, but  I was very confused as to what protein actually had to do with anything.