Title is a bit misleading. None of the scientists quoted in the article think there are too many eagles. The eider researchers say they found evidence of a link between increasing eagle populations and a decline in eiders due to increased mortality of nesting females. However they attribute that to eiders being forced into areas with more eagles due to a shift in their food source.
“But it’s not the eagles that lie behind this big decline in the population. That’s simply ridiculous to me.”
The caspian tern researcher mentions that the eagles attack the colony and pick the young ones one by one. But remember, these are caspian terns, at the edge of the their distribution in the baltic sea. The species wordlwide isn't endangered, but the population in the baltic sea is vulnerable. Should we aim to conserve all species, everywhere where they occur? I don't think so, especially not in marginal areas for the species.
The less white fronted geese research is a different story. This is a globally endangered species with <620 birds left. This is almost so low that you have to start thinking about protection at individual level. The main reason for their decline was heavy hunting pressure on the eastern parts of their migration routes. But with such a low population, and individual eagle targeting the geese when they moult can have a big impact. Is that because there are too many eagles? Or because there are so few lesser white fronted geese?
As to osprey, like the researcher says, when eagle numbers went down, ospreys occupied places formerly taken by the eagles. Now the eagles come to take them back.
And for black stork, this species has an extremely large range and the population is of least concern, and actually seems to be doing quite well, at least in parts of Europe.