Yes. It's a very good point that you make. Those are probably the three best examples of species that technically would be called invasive; however, we have found a balance with them in the ecosystem. They've become prized sport fisheries as well. We have other examples of introductions such as alewives, for example, that have become fisheries as well, but unlike the ones you mention, alewives continue to be problematic, in that they attack the forage base. They just continue to be a nuisance as competitors with our native species.
Those are probably the three exceptions. The invaders we typically have, such as alewives, zebra mussels, the spiny waterflea, and the sea lamprey, are ones that have continued to be our nemeses, because they compete with or attack our native species that are so valuable to the ecosystem.