Nothing, if it wasn't so expensive
Converting plastics and other trash to fuel would be great -- if it wasn't so expensive. Many other businesses have tried versions of this process, but so far nobody has been able to make it competitive with fuels refined from oil. It turns out it actually *is* cheaper to go to the ends of the earth to get our fuel.
Of course, the nice thing about all that plastic is that it will still be around decades from now if the process to convert it to fuel does become economical. Plastic is a very good way to sequester carbon...
As for all that plastic in the ocean, most of it has been broken down into tiny bits that would be impossible to collect. Scientists have to use fine cloth sieves to even collect it. While there are whole plastic jugs and other items floating in the ocean (especially since the Japanese tsunami), the idea that there is a Texas-sized island of these big chunks of plastics floating out there is just a scare tactic that the media does everything it can to promote.
