Differentiating "meat vs. plant" is too narrow of a scope - or too vague of contexts for comparison.
From my understanding in regards to meat consumption and demographics who eat plant-based, these two fundamentals issues exist:
1) Burnt red meat produces carcinogens, and
2) it's the other food that the majority of people eat as part of meat [e.g. a burger with a bun + sugar-loaded ketchup etc], as part of the industrial complex-driven Western diet that are, where people who eat plant-based are likely more conscientious about the food they are overall vs. the general population who eat meat, where also I believe the majority who eat highly processed meat rather than straight animal product.
There are easily enough people and a growing body of carnivore diet followers that could facilitate including them as a comparison, but in reality there should be other groupings like ; and what about including measuring if the participants have historically done water-only fasting (and number of days on average), and number of water fasts they've done during the study period, etc - so then we can see if there's a chance in the distribution?
Such "complex" studies ideally need to have say 100,000 to 1,000,000 participants to get enough diversity - and we'd also want to be careful that the studies aren't co-opted or influenced-captured by industrial complexes and their own interests.
It'd also be ideal to include as part of the participant cohort dietary changes for willing participants, say switching 1,000 to 10,000 people to high-quality high-fat red meat - who perhaps have other arguably healthy diet-behaviour changes to how that cohorts distribution changes vs. the general population.
The issue with such a study is you'd need to subsidize some participants is industrial complexes have maximized accessibility to low quality-harmful "foods" - maximizing profits too to maintain market dominance by also having more profits/money to advertise to remind people to buy their brand - and so high-quality red meat, for example, is too expensive for most people to switch to - even if the long-term cost of cancer treatment and loss of productivity far outweighs the higher initial cost; and so industry isn't going to pay for such a study, it would likely have to be heavily funded through philanthropy.
But to me that feels like a distraction, because have you seen what vegans eat? vegan pizza with "fake cheese", vegan burgers, highly processed hummus on a daily basis, etc.
From my own observations, almost all vegans I know are vegan for ethical reasons, not for health reasons. The fact that it appears to be healthier is just a nice bonus. Therefore, claims that plant-based diets are just healthier because they don't ever burn their burger or put sauce on their bun, feels incorrect to me.
Key word here, appears to be.
Upon deeper study, from what I have read, people who transition to vegan on average start having health problems related to the diet at an average of 5 years into the diet.
Note, a vegan diet is very different than a person who at least will still consume eggs or drink milk, etc.
Self-reporting may also be a major issue here as well, as it's possible that someone who is doing something for ethical reasons may put their cause above the ethics of being honest or lying; and metrics for health for the vast majority of people, especially if simply observational studies, aren't adequately or thoroughly gathered in the vast majority of cases; and especially long-term and qualitative comparisons on quality of life haven't been done yet - so the "appears" to be healthier could simply be a person feeling better because of feeling good for the ethics of it, no?
Re: "Therefore, claims that plant-based diets are just healthier because they don't ever burn their burger or put sauce on their bun, feels incorrect to me."
That's a straw man argument, I didn't make that claim.
There are proteins in meat that turn into carcinogens when burnt - I don't know if that's the case with whatever the plant-based "burgers" / patties consist of, if they turn into carcinogens from being burnt.
There are more counter-arguments to other things you state but I don't have time at the moment, e.g. your food examples of what vegans may it, they may also eat far less food than the average meat eater - which provides less food-energy for potential cancers, where it's known that lower calorie intake over a lifetime appears to also be a factor for life expectancy.
E.g. "The researchers found that people who cut their calories slowed the pace of their aging by 2% to 3%, compared to people who were on a normal diet. That translates, Belsky said, to a 10% to 15% reduction in the likelihood of dying early." - first google result for me, https://www.nbcnews.com/health/health-news/calorie-restricte....
It's one of these complex topics that no one has yet organized into a proper-complete distribution of arguments and counter-arguments, to lead towards designing adequate clinical trials to get definitive-scientifically derived answers - and that aren't perverted by influences of industrial complexes.
It's likely that self-reporting is indeed an issue, but I wonder whether it's not a "balanced" issue on both sides. E.g. there are so many people who want to eat meat, they might be willing to lie about their health when asked how meat affects their health.
So maybe this is a myth perpetuated for burned meat, too??
Indeed. There's also the issue of lean meat vs. high-fat meat - where the body needs and benefits from the fat concentration being there as part of digestion and proper nutrients, along with another significant difference between white meat vs. red meat consumption.