In the short term beavers and their dams can be a nuisance and here in Wisconsin, beaver dams have caused flooding of roads and then the DNR dynamites the dams. Private land is flooded much to the owners' chagrin and then the owners have to take measures to get rid of the beaver.
When I was stream trout fishing in northern Minnesota and Wisconsin for many years, fresh {no more than 2 or 3 yrs old} beaver ponds were prime waters for catching brook trout. After 2 or possibly 3 years, the flooded trees and bushes died and no longer attracted insects which the trout fed on, so the ponds no longer held trout. Also...for some reason, beaver just like to "gnaw" down larger trees and reach out quite a distance to do this.
After awhile for various reasons, the beaver dams opened up, the water level dropped and the stream once again became evident.
What was left along the stream was grazing land for deer and elk....which is beneficial to not only the animals but also for man. This is the long term benefit of beaver.
Because of the impatience of our times, increased human populations and a limited amount of "wild country", beaver have become a modern day nuisance.....and, we just don't tolerate "pests"....Fred