Also, that plastic is really the lowest possible grade of plastic that you can imagine. I'd be surprised if it were good for even synthetic mulch in playgrounds.
The plastic is already killing sealife and will continue to do so as long as the plastic is there. Filter the sea, maybe some creatures dies, but future generations will not be killed by plastic.
It seems reasonable that the gyres have always collected crap and sealife has avoided it. Now that crap is plastic.
But, the gyre already provides the function of avoid-getting-killed-by-plastic, so it's not clear why we should aggressively reduplicate that effort.
The garbage patch may offer benefits to the ecosystem which are not immediately obvious. Whereas, filtering is likely to damage the ecosystem in some ways.
Human record of tending to the ocean has not been very good and we're not good at predicting consequences. I recommend watching documentary film "The End of the Line" http://www.imdb.com/title/tt1176727/ before assuming that filtering is a panacea.
Gyres collect it, we harvest it on the spot.