The problem is that the ecosystem is so interconnected. The salmon numbers are down because of over harvest, habitat destruction, and (now) lack of food in some parts of the ocean. Chinook and coho are "suffering because of increased pinks. Not to mention climate changes.
Killing the seals will allow them to increase, which might benefit if they have sufficient food. If not, no benefit. They might come back in bigger numbers have crappy places to spawn. No benefit.
The seals may be also eating something else that is keeping a lid on, say, Humboldt Squid.
We too often manage in what are called silos, bunkers made of very strong concrete that resist the penetration of new ideas.
We need to understand that removal of the seals will "fix" one short term problem but is not dealing with the overall picture. Unfortunately, that is also why we do nothing because no one thing, other than removing 90-95% of earth's humans, will fix the problem.
90-95% may be extreme. I think it would really help if we could select for stupidity and general tendency to do evil in the culling of humans. Granted, that only leaves about 30% left over (and I'm not sure if I'd make the cut), but that's less bleak than 5-10%.