You're not wrong, but there are limits. Just cooking food involves denaturing organic compounds and produces toxins and carcinogens, and we've only been cooking foods for the last hundred thousand years or so, not long enough to evolve more than cursory resistance. Many of the compounds produced are identical to the solvents and plasticizers you're worried about.
That's like saying, "Everything has moisture in it, so why should I worry about my kids going near a pool?"
Sure, but like I said, cooking meat already produces similar compounds. If you're an absolutist, then you don't want to cook meat. Otherwise, it depends on how much more of those compounds plastic would contribute. If it's 10% more, that's one thing; if it's 1000% more, that's another. I suspect it's closer to the former with the current standards in the US but I could be wrong.
As far as I know the US does not have any legal or regulatory requirements on plastics in contact with food.
A quick google (yeah, I still use it :-P ) brought this up:
https://www.acplasticsinc.com/informationcenter/r/fda-approved-plastics-for-food-contact
and
https://www.fda.gov/food/food-ingredients-packaging/packaging-food-contact-substances-fcs
(post is archived)