4. Farmers are already facing great difficulties from economic shocks like Brexit, Covid, Ukraine and Hormuz in a short span of time, and further strain is unwelcome.
There will always be some reason against a measure that doesn’t immediately benefit humans in the short term but yields benefits in the long term.
Eagles are also dealing with other stuff (arguably more significant-- e.g. habitat loss), but that's an irrelevance to this issue.
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.