The large coal deposits of the Carboniferous may owe their existence primarily to two factors. The first of these is the appearance of wood tissue and bark-bearing trees. The evolution of the wood fiber lignin and the bark-sealing, waxy substance suberin variously opposed decay organisms so effectively that dead materials accumulated long enough to fossilise on a large scale. The second factor was the lower sea levels that occurred during the Carboniferous as compared to the preceding Devonian period. This promoted the development of extensive lowland swamps and forests in North America and Europe. Based on a genetic analysis of mushroom fungi, it was proposed that large quantities of wood were buried during this period because animals and decomposing bacteria had not yet evolved enzymes that could effectively digest the resistant phenolic lignin polymers and waxy suberin polymers. They suggest that fungi that could break those substances down effectively only became dominant towards the end of the period, making subsequent coal formation much rarer.
So indeed, superficially, a few parallels can be drawn to the anthropocene "plastic age". Some life form (trees) essentially "trashed" the planet with polymers that were not biodegradable. It took 60 million years until evolution "caught up" and equipped bacteria and fungi with the enzymes that could degrade those polymers. Nowadays dead trees in a forest rot within a few years.
It seems reasonable to think that the same will eventually happen to our plastic; i.e., if we were to cover the planet in plastic waste, then eventually, after a few million years (or far sooner, if there are only few mutations required for the polymer degrading enzymes to be efficient with plastics), some bioform will be able to feed on that.
[1] https://en.wikipedia.org/w/index.php?title=Carboniferous&old...
Also, why is plastic being burned? Separate it cleanly and just store it in packages in a landfill. Either eventually a method of recycling will be found so the landfill can be harvested again for raw materials, or a bacteria will be found for that specific plastic that can be released on there.
As it stands, there's trash separation (in developed countries) and then whatever can't be recycled either goes to a landfill or burned.
Really you'd be cleaning up the landfill more than mining it, but that's okay.
A lot of recycling decisions come down to similar considerations, doing them is a net drain on resources and costs money, so it doesn't make any sense.