  We tackle the question of whether regular black holes or other alternatives
to the Schwarzschild solution can arise from an action principle in quantum
gravity. Focusing on an asymptotic expansion of such solutions and inspecting
the corresponding field equations, we demonstrate that their realization within
a principle of stationary action would require either fine-tuning, or strong
infrared non-localities in the gravitational effective action. This points to
an incompatibility between large-distance locality and many of the proposed
alternatives to classical black holes.
