My understanding is that similar benefits of access to meat were gained from learning to cook in general, as well. While meat likely contributed to humans being able to advance as a civilization and perhaps conferred various physiological benefits, the skill of cooking in general allowed us to extract more nutrition from a lot of foods we'd otherwise spend a lot more time chewing and digesting.

Getting nutrition from food faster, with less energy, is a huge deal. Whether it's meat or not, being able to feed young children easily digested, high-calorie food is a huge advantage. Being able to feed anyone is a huge advantage, but in particular weening children earlier would have freed up mothers to reproduce more and/or do other work. Humans becoming more independent earlier is a major factor in humans being more productive in many of these studies.

I haven't read about this for a few years, but as I recall it doesn't seem that the protein/fat components of this development were the essential factor for moving people forward. We're able to get plenty of calories and nutrition (including protein) from plants, but only if we cook it. Meat certainly helps, but isn't required in the equation.

I'm opened to being corrected – like I say, I'm probably out of date here. I'm not sure what evidence could have changed this, though.