I've looked for info on why we don't use plastic for carbon sequestration, and haven't found anything significant. It seems like land-filling plastic, or minimal processing (compaction it melting into a more dense block form) might be better than attempting to recycle it all, once sequestration is taken into account.
Also, I suspect we'd be better off right now if we'd been land-filling plastic, instead of shipping it overseas to be burned, shredded, littered, dumped, or even discharged at sea. Even official estimates claim minimal percentages are actually being recycled, before accounting for fraud.
We might have significant reduced levels of micro-plastic in the ocean, and a greater amount of carbon sequestered, instead of the high cost and seemingly minimal benefit we've seen "recycling" plastic.