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.
2) The NPGP is very thin (non-dense). It is not a solid pile, but rather an enormous area where trash dots the ocean here and there. Trash is always within eyesight, but rarely within reach. Thus, accumulating a significant amount of trash is a very difficult and expensive process, as it requires skimming a huge area (while paying the high costs of ocean operations).
3) Plastic resists salt well, but it is quite vulnerable to sunlight – it degrades steadily. Thus the plastic in the NPGP is likely to be substantially lower quality, as a material, than plastic in a landfill.
Due to (1) and (2), the cost of obtaining the trash from the ocean is MUCH higher than from a landfill (I’d guess between 100 and 1000 times more expensive). And due to (3), the result is much lower quality plastic.
I don’t follow the recycling world closely, but I have not heard of it being a profitable field to purchase and recycle landfills, even though the costs there are literally orders of magnitude lower. Certainly some recycling of materials on land can be done at a net gain in energy / materials, but the gains are slim enough that adding significant extra costs eliminates them, and renders the whole cycle as net negative, which makes it destructive of resources. The enormous extra costs of getting the source material from the NPGP dwarf the slim margins of recycling, which means that recycling that trash would use up far more resources than it would generate.
Another way to think of it is in terms of the ocean tax vs. the land tax. The ocean tax is the extra cost of doing an activity in the harsh, remote, corrosive environment. The land tax is the extra cost of dealing with regulations, bureaucracy, and other land-specific costs. As the ocean tax is generally quite high, it is only profitable to do things on the ocean where the ocean tax is relatively low and/or the land tax relatively high. For example, when transporting goods, the land tax is extremely high because moving big masses of stuff is much more expensive on land. Or establishing a hospital, where the regulatory cost on land is very high. But for recycling, the ocean tax is extra high (you have to somehow sweep up this huge body of widely dispersed material), and the land tax is very low (there’s nothing illegal or extremely difficult in buying a landfill in order to recycle it, or buying up plastic waste that people are generating). So if recycling ocean trash ever happens, it will be one of the last things to be done on the ocean, not one of the first.