The crab fishing is highly regulated. I’m no expert, but just from watching “The Deadliest Catch” on TV I can see that there is a very strict and short season on the different crabs they harvest. That might have recently changed from a very short season (on the order of just a couple of days) for many boats to a set weight quota for a smaller number of boats. At any rate, it’s not just go out and catch all you want, any time you want.
Still, from the Alaska Department of Fish and Game
Oddly enough, I doubt that fishing would cease if it became unprofitable: for one, like farming, fishers would demand subsidies until they were profitable. Two, also like farming, the urge to do so for some people seems hardwired into our genes: many family farms continue to go at it despite very little profits. (And at the point where many commercial companies would cease to fish, the damage that small-time operators could do would still be substantial.)
Not all species are sustainable at low populations. If they continue in their hardwired habits they might not have as much a chance individually to breed given the low populations. And the predators that mainly feed on them will still have the same need to feed on them.
Which is not to say that fish, or any given aquatic species, is the be all end all of human importance. But if fish extinction causes a chain reaction that leads to the disappearance of algae which provides the majority of the world’s oxygen (through a boom-bust cycle driven by a lack of predators, for instance,) it could be very bad, to understate things.
“Would”? Heck, in Canada we have that now. The federal government spends a huge amount of money essentially paying fishermen to not fish and not find other jobs.
For any fishery regulated by the Alaska Department of Fish & Game, it’s a pretty safe bet to say that it’s being managed well with an eye toward long-term sustainability. I worked as a deck hand on a salmon boat out of Dillingham for a couple summers. In that brief time I saw that ADF&G is very serious about the long-term Alaska economy and has very real power to enforce its will. Penalties for fishing in the wrong place and the wrong time are swift and costly, up to and including confiscation of your boat and license. (Salmon boats at the time went for about $250k on average, as did licenses. Those costs were, of course, on top of lost revenue from not being able to fish.) The places and times fishing of a species is allowed are carefully selected to ensure that enough of that species gets a chance to spawn and replenish the stock for future years. They seem to have no shortage of manpower or political clout to carry out their mission, which in fishing terms is the long-term health of the fishing industry in Alaska.
Where the Alaska fisheries have problems is in those areas where a given fishery falls outside of ADF&G’s authority for part of the species’ life cycle. Salmon, for example, spend a substantial amount of time in international waters, where a state agency has no authority. High-seas overfishing is a real concern and mitigation depends on international treaties, which I was told tend to be less strongly written and do not have the enforcement levels that Alaska regulations do.