"Would need some sort of high-volume filtration system."
Yes it would, and wouldn't that be an extremely intertesting bit of technology to develop? Right off the bat if they first developed a way to get the plastic to reclump together, then the filter, then be able to further refine it, it could be a very lucrative oceanic mine for decades, like has been mentioned, get some fishermen and sailors back to useful work. And similar high volume filtration tech might be used for another example say in cleaning up fresh water sources better, or to be part of waste water treatment plants. We already have filtration systems for this or that, but to develop something that could work on that sort of scale could very well be some important tech down the road. And like was pointed out, being plastic, this could help develop interest in larger scale energy plants that could use the stuff, including th..terraforming isn't the word, aquaforming? Huge floating energy conversion barges. Or just concentrate it back down so it could be used for..manufactured plastic goods. I don't see the need for plastics going away anytime soon, nor the need for more forms of energy. And we need *work* for millions and millions more people planet wide every year, something useful.
A lot of times I think we humans might be better off just with a 180 attitude adjustment, instead of always looking at things as problems, if we just looked at them as opportunities, it might make solutions appear easier and work better. The old saw of how to look at things, the glass half full or half empty deal. Turn the "Oh, noes!!" into the "Hot Damn!"s.