This article seems to take more of an anthropologic perspective. It's true that if we wait long enough, the nature will settle down the issue on it's own. However, are we willing to make the short-term sacrifices? The main issue of the so-called invasive species is that they don't have a natural competitor in a new environment, therefore they will become dominant if left alone. Their overgrowth not only disrupt the variety of the local vegetation world, but also the balance of the animal world, sometimes including us. For instance, the potato famine in ireland: The potato plants across Europe were originally transplanted from Peru, they became the main source of food in Ireland. Since there was no diversity of the plants, when potato blights happened, it destroyed all the potato plants, and caused a catastrophic famine with 1 million death toll. So, in a way, the nature did take care of itself, but with a great cost of human lives. This might not be the best example of the invasive species, since the active human agriculture was involved. In the end, humans always lose the war to the nature no matter what. The control of the invasive species may help a little, but unless human migrations are completely restricted, the invasive species will have their places.
Yes. Towards the end of the article, the author points out that the debate isn't really over whether species which overwhelm an ecosystem and threaten most other species there are harmful or not. They all agree these things are a problem. The argument is over whether we should see any transplanted species as dangerous or whether we should only see some transplanted species as dangerous. As dynamic and unstable as ecosystems tend to be, I'd rather we erred on the side of the conservationists. Organisms will migrate, and they'll inevitably bring other organisms with them, but since we have the ability to manage this, to some degree, we probably should, even if it's only to keep an environment friendly to us around as long as possible.