Right. I'm not asking about studies about people that may or may not have chose veganism/vegetarianism at a certain point, but about large groups that exist that way for significant periods of time. People that seek out a certain diet are going to show better quality of life than people that don't, regardless if it's veganism or not.
I think the difference is largely uninteresting in this debate. Personally I enjoy eating meat and don't see myself giving it up entirely. I think there is a reasonable middle ground between 'we continue eating like we do now' and 'everybody will be forced at gunpoint into a vegan diet'. We could save enormous amounts of pollution and animal suffering by simply eating less meat. The existence of significant populations who have been living successfully as vegetarians or vegans for thousands of years simply demonstrates that we should not be overly concerned about side effects of reducing (not halting entirely!) our meat intake.
Suppose we (as in "the average first-world citizen") were to collectively half our meat consumption. Either by reducing portion size, or by eating it less often. The benefits would be amazing, and apart from people who make their living selling meat I don't see any real downsides.
Back when I was growing up I was used to eating meat virtually every day for dinner. These days I skip a few days each week, because I learned how to cook different stuff (and these days I have to pay for it myself, instead of my parents...).