Protein is a major appetite suppressant. I'd read this but never really realized how true it is until starting on a protein heavy diet. I now eat near 500g of chicken breast a day, and by the end of the day I'm basically having to force feed myself. Yet 500g of chicken breast is less than 800 calories! And the other stuff is just to balance out my diet.
And I love eating as much as anybody else. But you simply cannot eat that much when you're on a protein heavy diet. Finding data on protein consumption rates over time is difficult, but I'd hypothesize we were probably much higher on effective protein consumption in the past. I know absolutely nobody that regularly had something like 'steak and eggs' for breakfast, yet it seems that was indeed a thing at some point.
[1] - https://en.wikipedia.org/wiki/Digestible_Indispensable_Amino...
Meat consumption is associated with higher BMI: https://pubmed.ncbi.nlm.nih.gov/32443920/ (summarized in: https://www.news-medical.net/news/20200615/Vegetarians-have-...)
Something you have to keep in mind in modern times is also food processing. A 10 piece set of McDonalds chicken nuggets weighs around 163 grams, but contains only 23g of protein. By contrast 163 grams of chicken breast contains just about exactly 50 grams of protein. The more processed something is, the more it tends to drift from its nominal nutritional value, and it's safe to say that a much larger chunk of people's "meat" is also coming from these sort of heavily processed meat-like foods.
As for the studies, you have a common bias they suffer from. You're comparing some group of people opting into some diet or another, versus the population at large. An apples to apples comparison would be something closer like comparing those on a long-term vegetarian diet to those on a long-term carnivore or keto diet. The idea is to just make sure you control for the "I care about my diet and have sustained dietary self control" variable. Unfortunately actually controlling studies means you'd get far fewer exciting headlines and bullet points for our CVs.
[1] - https://www.pewresearch.org/short-reads/2016/12/13/whats-on-...