Just before the fish is extinct prices go up so high that every fisher wants to catch some. This has (almost) happened to cod a few times and is about to happen again, for the last time I fear.
Any economic system needs to deal with supply/demand panic situations. Socialism will use a government panel to determine supply and demand ratios. May help avoid foreseeable catastrophe, but also can ruin private industry and leads to graft. In your example, you assume higher prices will not change the consumer demand. Once people refuse to pay $30.00 a pound the market will reject more supply. If people "need" their cod you would see cod farming develop to help meet that need. next might be cod imitation meat like with crabmeat. Your argument is that we may run out of cod before the price can rise enough to stop demand.....hard to see that happen only by fishing, the risk is that a fungus quickly knocks out a generation of cod. Always a risk, even to humans.