I knew something didn't add up here. The economics of the article didn't make any sense until this line appeared.
Basically, it's saying subsidies have removed the free market's inherent protection of resources. Governments are keeping prices low when demand is high. Of course that's going to lead to overfishing.
This article's recommendations are basically just more socialism. That may be necessary due to Europe's increasing addiction to subsidies. But the most obvious and quick solution would be to remove the stupid subsidies.