I spent 6 years in the Navy and I believe most of the ships now have incinerators but in the past they did not. And once you are great than 50 miles from land in international water it all goes overboard. I say this because I wonder if vacation cruise ships and other cargo ships have the ability to burn the garage they make. If not they maybe a large source of ocean trash.
We have one incinerator near us that burns trash and makes electricity. They are getting large enough they are taking other cities trash so I think your idea will happen but probably at a slow rate.