From what I have read, fishing raptors, such as eagles and osprey, need flight room to swoop in on the waterbody in which their prey reside. They rely on their superb vision. A cover of trees, shade cloth, shade sails, screening, etc. interferes with both their line of sight and flight zone. Smaller carnivore birds, such as kingfishers, can be a greater worry in the areas where they nest.
The one fish-eating bird I've not read something about attacks on koi ponds is the anhinga ... which, for those who are unfamiliar with them, dive into water and are able to swim underwater to catch fish. I'd guess that most koi ponds are too shallow for diving.

... but I'd expect breeders to have problems with anhingas.