When the population collapses, the species will go extinct.
The bigger risk extinction wise isn’t that we’ll fish a species to death, it’s that we’ll leave it in such a rough state that any number of random events might finish the species off.
Many fish and bird species have shear reprodutive ability as their only defense. In the case of Passenger Pigeons, they had very little defenses against predators, but migrated in huge flocks of hundreds of thousands at a time. No predator could really harm the flock as a whole.
Well, until Humans became too good at hunting anyway. (Also, USA used to be covered in forests. But we cut those trees down to make room for our cities)
As described in 1813 (From Wikipedia):
> The air was literally filled with (passenger) Pigeons; the light of noon-day was obscured as by an eclipse; the dung fell in spots, not unlike melting flakes of snow, and the continued buzz of wings had a tendency to lull my senses to repose.
https://books.google.com/books/about/The_Once_and_Future_Wor...
But with that being said: I like Talapia. I like Salmon. I like various fish. They're all quite tasty, and I'd like to keep eating them throughout my life (and possibly let my children have a chance at it too).
For people who liked one food: the passenger pigeon, that opportunity is now gone, because the species has gone entirely extinct. And overhunting of that species is cited as a potential cause for extinction.
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It has nothing to do with naturalism or the state of things. Just from a purely selfish point of view: if you like a certain food source, you have to take care of it, lest it goes extinct and disappears forever.