To support enough prey for an eagle, the ecosystem needs half a million calories.
That means every pair of golden eagles needs a huge territory.
So that's the reason I've never seen one: there simply isn't enough food in the ecosystem to support a lot of eagles.
Now let's do a thought experiment.
You would have to travel all over the world to get enough calories.
In the harsh conditions with little food, it has adjusted to survive with little protein.