2. Farms that keep sheep have more than one lamb.
3. The government doesn't, and shouldn't, intervene to protect people against every single risk they face in business.
Your statement is completely unrelated with the parent article. Contrary to what you say, the golden eagle is by far the best known species of eagle and the one with the greatest cultural importance.
The golden eagle (Aquila chrysaetos) is the species of eagle that has become the state symbol of the late Roman Republic and then of the Roman Empire.
Inspired by the Romans, during the last couple of millennia many other states have included the golden eagle in their heraldic symbols and several of them are still using it today.
Even much earlier than the Romans, at all Indo-European people the golden eagle had a special importance, being the bird used as a messenger by the God of the Sky, later known as Zeus in Greece and as Jupiter at the Romans. Already the Hittite texts from 3500 years ago have many references to the golden eagle.
The golden eagle is also the species that has been the most valued as a domesticated hunting bird in Central Asia.
The use of the "bald" eagle by USA has also been inspired by the Roman golden eagle, but the original species was replaced with a native American species. The golden eagles have survived in small pockets spread over a very large area from Western Europe to USA, so they were not representative for USA alone.
While the sea eagles, to which the American "bald" eagle also belongs, are bigger than the golden eagle, the golden eagle is stronger for its size and she is able to hunt bigger prey in proportion to its size. Only some jungle eagles, like the harpy eagle, are definitely stronger and able to carry heavier prey.
Or in Palestine, for that matter.
There was nothing unremarkable about the great plains (note the name); they didn't produce the crop yield that you value, sure, but that's not the only possible metric to measure anything against.
I think farmers are great; I don't think we should exterminate countless species to save them from one of the extremely-predictable externalities of their jobs.
The potential predations of a small number of eagles nationally will make very little difference to the enormous number of sheep kept by a large number of farmers. They can handle the strain, and if it's really somehow too much, there are mitigations short of extinction available to them.