Distribution level voltage is anywhere from 4kv to 25 kv. Say it's 12. Typical partridge or linnet distribution conductor might do 200 A. P=sqrt(3)IV cos theta = 1.73 * 200 * 12000 * 0.9 = 3.7 mw.
So you are correct your average distribution feeder probably does not have capacity for a 10 mw service. I guess that's not much of a shock.