Tires get more efficient every year, dust has reduced as the companies compete to make them last longer, and we're finally seeing the tire industry respond to pressure to reduce toxic runoff. Michelin's been removing phenols, for instance: https://resicare.michelin.com/news/michelin-resicare-resin-1...
Of course if you burn trash none of that matters, but it's already illegal in pretty much any advanced societies.
FWIW, I think - based on not feeling my throat close up most of the time - that the number of people who do this is small.
The old oven remained though, and was used as a self-emptying trash can. When it filled up, a fire was lit to empty it. I don't remember what the sorting rules were (I assume "does it burn well and not smell up the apartment too badly when lighting it") and how common plastic packaging was back then, but I'm sure that the emissions coming out from the chimney were not a concern.