Most disposable plastic is not PVC. Because Chlorine prolongs the life of the plastic, it's specifically used on things that you don't throw out.

In any case incinerators can handle the chlorine - it's so reactive that it's actually very easy to filter.

> You can't really "burn up" heavy metals

There are no heavy metals in plastic, and very little in consumer waste as a whole.

> are "solid hydrocarbons" but most plastics are more complex than that

But those 3 you listed are the vast majority of the thrown out plastics.

Municipal waste has a large fraction of waste from demolished buildings which includes wood, concrete, bricks, all sorts of stuff. PVC is a significant part of that waste because it is used for siding, floors, etc.

In a consolidated municipal waste stream heavy metals are a concern because they concentrate in the ash which has to be carefully stored. This kind of system

https://en.wikipedia.org/wiki/Plasma_gasification

is supposed to encapsulate heavy metals into slag particles that aren't very mobile and can be incorporated into roads, building aggregates and such but people have struggled to make them work, part of it is that the syngas plant and whatever uses the syngas and cleans up the syngas and/or the products of using the syngas is a chemical factory that depends on the inputs having a certain composition and the composition of a municipal waste stream is not at all constant.

PET is a major thrown-out plastic that's not a hydrocarbon, it's also the most recycled. Polystyrene, funny enough, is easy to chemically recycle but not through pyrolysis, it's the sort of thing you might even demo in a high school chemistry class if styrene wasn't so carcinogenic. It's never caught on because expanded polystyrene is hard to handle, transport and bring back to a chemical factory large enough to efficiently consume.