PTFE? It’s so non-reactive that it is commonly used in medical implants, precisely because of its high biocompatibility. I don’t think that there are any connections at all between PTFE and cancer.
"While PTFE is stable and nontoxic at lower temperatures, it begins to deteriorate after the temperature of cookware reaches about 260 °C (500 °F), and decomposes above 350 °C (662 °F).[58] Over 400 °C (752 °F) pyrolysis occurs and more decomposition becomes significantly more rapid. The main decomposition products are tetrafluoroethylene (TFE) and difluorocarbene radicals (RCF2).[58] The degradation by-products can be lethal to birds,[59] and can cause flu-like symptoms[60] in humans—see polymer fume fever."
It seems like a burner left on a dry pot or pan could easily do that.
Grills with PTFE coated utensils.
Commercial kitchens using specialized ovens and PTFE lined pans could be constantly putting out fumes.
Our propane pizza oven gets up to about 400C on the stone, and hotter at the flames. I don't think there's ever any PTFE near it, though. There do exist "non-stick" pizza peels, though, so someone could do that. The thing with peels on pizza stones is that their edges tend to grind down. I probably eat a miniscule amount of aluminum each time we make pizza.
You don't, at least not on purpose. At 390 C you're filling your kitchen with smoke, and if you're cooking on gas you probably already have a grease fire on your stove.
However, it is shockingly easy to get a pan this hot by accident, with no more than a few minutes of inattention. I've seen people burn the non-stick coating off their pans on a couple of occasions after getting distracted by the phone.
It's risky to use nonstick cookware the same way you use bare metal pans, by heating the pan up to searing temperature before adding oil and food. I tell people to treat nonstick as though the food is already in the pan before they turn the heat on: don't turn the heat up high enough to burn the food, and the coating will stay safe.
It's worth pointing out that there isn't really any good evidence that fumes from burning PTFE cause permanent damage. There have been very few cases of verifiable PTFE "fume fever", in spite of the fact that lots of people burn up their nonstick cookware, and lasting effects haven't been obvious as far as I know.
there are many pet horror stories of bird deaths from PTFE pans, typically from accidents, but occasionally from normal use. one may assume that it happens quite often without a canary in the kitchen so to speak, and thus goes unnoticed.
also, damaging the coating is known to lower the temperature at which PTFE will pyrolize. anecdotally i don’t think i’ve seen a single teflon pan in anyone’s home that didn’t have some damage unless it was nearly new.
most situations that people are exposed to PTFE fumes are certainly below the level that triggers acute illness, but i wouldn’t be surprised if it was very common to get enough exposure to contribute to cancer, but it would be very hard to verify or test for that specific cause.
Yes, it becomes toxic at high temperatures, same as many other commonly used materials, eg. wood. Should we also be concerned about widespread use of woods because it becomes toxic when burned?
Cookware is not designed to go to temperatures as high as those that cause decomposition of PTFE. But, there is plenty of wood cookware in common use. Spatulas, pot handles, etc.
https://en.wikipedia.org/wiki/Polytetrafluoroethylene#Safety