The suggestion of recycling the North Pacific Garbage Patch into building materials gets made a lot. While creative and elegant, with a little examination it turns out to be completely economically unfeasible, and actually wasteful of resources.
Think of it this way. Suppose it were possible to profitably turn trash into building materials. The most efficient way to do this would be to buy a landfill and recycle it. Compared to this strategy, using trash from the garbage patch has a number of major disadvantages:
1) Operating at sea is very expensive.