Your edit is where the problem is. Sure there is a lot of plastic in the ocean, but the ocean is big as well. As a whole the size of the ocean cancels out your attempts to do any recovery. You end up using more energy to power the filters (which are typically on ships) than you would by taking the oil powering the filters and directly turning it into plastic.

Plastic in the ocean isn't an easy problem to solve with anything other than wait for it to degrade. Which isn't as bad as it sounds because plastic doesn't do well in the sun, and we can easily make plastics that do worse and thus degrade faster.