It turns out that a lot of the plastic in the ocean is there because there are countries where people are just dumping trash in the ocean. It can be less expensive than transporting it to a dump and dealing with it there.

The answer has to include making waste plastic have enough value so that people find it advantageous to recycle it or at least to bury it.

But some observations on your comment.

Is plastic, that was never in the atmosphere (for millions of years anyway), really a carbon sink? It seems that trough its entire lifecycle it never goes into the atmosphere.

Also, if you burn plastic you’re displacing oil that wouldn’t otherwise be burned. Oil that is never extracted. And don’t forget that it takes a lot of energy to extract oil, so burning plastic reduces CO2 emissions globally somewhat.

Also, I’m skeptical about the practicality of using landfills to create geological treasures for mankind 100k years from now. The problem with it is that I feel that it is wishful thinking that placates our conscience. It’s easy to imagine yourself living “sustainably” in geological time scales. It’s hard to live sustainably in 1000 year timescales.

Burning is the only thing that makes sense, and that's OK if thebtotalt amount is "not too much", where current fossil fuel usage is "too much".