In theory, if this was considered a big enough problem, yes - the market would resolve this. And by "big enough problem" we have to remember that market-driven economies respond to market demand forces.

Plastic in the ocean is definitely a huge problem, but it's not a market problem - not yet. When consumers are willing to pay to get plastics out of the ocean, hundreds of companies will appear eager to solve the problem.

There's a comment above (@pdpi: "At what timescale?") that identifies the issue at hand. In this case (and in a lot of cases) we need regulation because market demand to solve this isn't fast enough (or may never exist)