Bernard R. Ortiz de Montellano answered the protein hypothesis in Science in May 1978, and the answer was arithmetical rather than rhetorical.
Tenochtitlan was not short of food. The city drew very large quantities of maize, beans and amaranth as tribute from the provinces, and it worked chinampa agriculture in the lake beds at high yield. Those two sources between them were sufficient for the population. Maize and beans eaten together supply complementary amino acids, so a diet that looks poor in animal protein is not necessarily poor in protein.
The distribution was wrong for the hypothesis. If the practice were a response to protein scarcity, the flesh would have gone to the people who were short. It went to the elite and to those connected to the ritual, that is, to the best fed people in the city.
The timing was wrong as well. Scarcity in an agricultural year falls before the harvest, not after it. The concentration of the practice fell at harvest, which fits a thanksgiving far better than it fits a famine response.
There is a general lesson in the exchange worth more than the specific result. The proposition was rejected because it was specific enough to be wrong. A great deal of what is written about sacrifice in other people's religions is not specific enough to be tested at all, and that is a defect rather than a form of caution.