It appears, from a cursory 10-minute search, that humpback, fin and minke whales (that have been explicitly mentioned in this thread as being targeted by Japanese whalers) populations are ok (ie., the species' survival isn't immediately threatened) assuming current trends and restrictions. I looked up blue whales because they're the biggest. It isn't clear to me if anybody is targeting blue whales, but their numbers seem inordinately low. Sperm, or, interestingly, Moby Dick whales seem to be doing ok.
While it does seem to be the case that the Japanese are trying to be somewhat deceptive wrt their whaling practices, I want to suppose that they're on top of things enough that they're not going to hunt any particular (or, at least not all) species to extinction.
Is hunting any particular whale species to extinction that important? It seems like it might be, or should be, but I don't know what criteria might be used, other than decidedly emotional ones, to ascertain whether it is or not. For example, how does the oceanic ecosystem affect our survival, and how important are whales to that ecosystem? My guess is, not that important. Just like the survival, or not, of, say, Milwaukee, isn't THAT important. But, for some reason, I find the mere prospect of it quite alarming.
Why are the Japanese being deceptive about their whale hunting? Because there are international restrictions, and at least some oversight and enforcement regarding those restrictions, and because there's a lot of money to be made from hunting whales.
The numbers suggest that, with no restrictions in place, perhaps right whales and blue whales could/would be hunted to extinction in the foreseeable future. Wrt to other species it isn't so clear.
As to esthetic/moral, ie., emotional, considerations, I can imagine a world without any "wild and free" animals, but I'm pretty sure I wouldn't want to live in such a world. The preservation of a species, any species, seems to have some sort of intrinsic value to me. I don't have a rational explanation for this at the level of ordinary language. Anyway, if a person advocated the extinction of, and had the means to bring about, the extinction of a species such as, say, whales, then I'm pretty sure that I'd rather that that person die than that the species become extinct.
Blue whale population trends:
http://www.wisteme.com/question.view?targetAction=viewQuestionTab&id=8441
Blue whale Wiki:
http://en.wikipedia.org/wiki/Blue_whale
Humpback whale Wiki:
http://en.wikipedia.org/wiki/Humpback_whale
Fin whale Wiki:
http://en.wikipedia.org/wiki/Fin_whale
Minke whale Wiki:
http://en.wikipedia.org/wiki/Minke_whale
Japanese whaling Wiki:
http://en.wikipedia.org/wiki/Japanese_whaling
Whale species Wiki:
http://en.wikipedia.org/wiki/List_of_whale_species