Re: "The fact that it appears to be healthier is just a nice bonus."
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.