As someone who avoids cooking with plastic, I've always wondered... what makes people think it's safe? Does it not occur to most people that plastics can break down through the heat they're subjected to, or do they assume the plastics in question have been specifically designed to adequately withstand that?
To your point, I don't have any particular reason to think that trace quantities of plastics going through my digestive system are going to cause any harm to me. Obviously if I have specific reason for concern I'll be careful (I'm not, like, going to eat off of asbestos plates...) but otherwise I'm not going to think about it much.