There's a carbon cycle of plants -> oil -> plastics -> burn in air -> plants -> oil ... And that cycle takes a long time.
But the carbon cycle I am thinking of is one that makes the carbon in the plastics bio-available to plants directly. That means greater fertility, greater food abundance, food sovereignty, better land management.
Trying to stuff the carbon from plastics back into rock does not give us greater fertility, food abundance or food sovereignty. If anything, it will increase the wealth inequality gap, and makes it harder to feed everyone.
We're not quite there yet. The key is being able to safely composting plastics, and that means finding or breeding microorganisms that are capable of eating it. What we would have to give up are the properties of plastic that our modern society is addicted to ... something that _doesn't_ biodegrade, durable and cheap enough to be used ubiquitously.