The problem with capitalism is that it ensures that everything dies, and everything gets fished to extinction.
Imagine cod gets up to £500 a kilo. Will it stop the fishermen? Not a chance! Because the higher price ensures that people will still fish it! As long as people are prepared to pay money for it, then it ensures the fish will be wiped out.
See
Rare Tuna - Food & Dining (washingtonian.com) for an example of this - those Bluefin aren't going to last long. There is another one I read in New Scientist recently, where there is a fleet of boats that sail out *every day* to fish for a fish that is nearly extinct. Landing one of these fish earns the boat $600, and the fish will sell to a rich businessman in Japan, via various fences and ner'do-wells and, eventually, a sushi chef, for tens of thousands of dollars. $600 is more than the fisherman would earn in two years normally, working the land. Hence dozens sail every day, catching not even one fish a week between them!
Quotas make little difference to anyone, and, in fact, make things even worse. Imagine you are a modern fisherman, with your huge pot of crab, a table of iced cod and other fish, or whatever. You reel them in, and kick and squash the little buggers into the hold. If it isn't full enough to meet your quota, you carry on. Now, once you start getting near your quota, what do you do? You start only pulling out the more profitable species. So the smaller crabs, the eels, etc. get dumped, while the lobsters and bigger crabs get to take their place. But those smaller crabs and cheaper fish are half frozen, bashed and battered, and have a reduced chance of living any length of time.
And, if the boat simply meals (grinds them up) them before dumping, they can be to the pound accurate with the quota, even on the worst of trips! Yet when it's a good trip, they can replace them with higher value stock! With only a negative effect to the environment.
Size limits are also counter-productive. One big fish can produce a million or more roe, but they all get caught! The only selection pressure on a fish these days is to not be trapped by a huge net - get through the holes and live. Hence, fish are growing to size slower. This makes them more likely to be killed by a seal or whatever, as they are still subject to the normal selection pressures as well.
In fact, natural selection is still working too. The things that eat fish have a reduced food source, so they put more pressure on the few places that trawlers and net-draggers cannot go.
Eventually, every fish that wants to breed will end up on a Nemo style adventure to find another of his own species. And then that will be that.
Forget quotas. The *only* way to protect the Orange Rougher (or whatever) is to pass a world-wide law that limits the price of a fish to £5 (or whatever) because that destroys the incentive. You *have* to fish the common and easy to find species, or else you won't get enough fish to pay your wage bill.
The only other option would be to gene-splice some popular high-priced and rare fish (perhaps ones on the endangered list?) with something that causes temporary impotence, with repeated doses causing the "little soldier" to wither away. Then there would be no demand!