The tl;dr is that the protein deficiency hypothesis doesn't hold water. There are a number of competing explanations out there that each highlight different possible causes. What's below is adapted from a term paper I wrote for a Mesoamerican archaeology class. This isn't my area of expertise, but hopefully it gives you a good jumping off point.

The Aztecs sacrificed slaves acquired through conquest or commerce by cutting out their hearts. This sacrifice was carried out by a number of professional, elite priests and in public view. Accounts vary, but the extremities were the parts most likely to be eaten by people; the torso was given to the zoo to feed the carnivorous animals (Harris 1985). It is this form of sacrifice that garners the most attention, but it was not the only one practiced in Mesoamerica. Sacrifices of material goods, of small animals, and of one’s own blood were also common.

The Aztecs are unique in their conduct of xochiyaoyotl or “flowery wars.” These wars were ostensibly conducted to acquire warriors for sacrifice (Hicks 1979). Western explanations of war are clustered around the maintenance and expansion of political and economic control. The Aztecs seemingly were not attempting to increase their territory.

Michael Harner, an important figure in the cultural materialist school of thought, argued that xochiyaoyotl amounted to hunting expeditions. The captives were walking slabs of protein who, after capture, would deliver themselves to the Aztec capitals to be eaten. Harner’s thesis is predicated on the lack of domesticated megafauna in the Aztec area. With no domesticates, and therefore no easy access to animal protein in the form of meat and dairy, the Aztecs were reliant on maize and beans for essential protein. Maize and beans are sufficient sources of amino acids, but only in relatively large amounts and only together. A failure of either crop meant disaster (Harner 1977). These periods of crop failure precipitated a call for more sacrifices from the priests. The priests and other elites would then have access to the thigh meat of the sacrifices, mitgating the negative effects of the famine. Elite status overlapped with, and could be gained by, personal military success. In Harner’s explanation the Aztec elites guaranteed dinner, at least for themselves through ceaseless war.