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.
In the United States the normal distribution voltage, prior to being stepped down for consumer use, 7.6kv phase to ground, 13.2 phase to phase. So yes, you're pretty close, except the 13.2 kv would be 3-phase. For heavy industrial use, 4.4 kv is common for actual end user equipment, but above that would be some pretty serious equipment for an end user. Larger transmission lines operate anywhere from 60kv on up to 1.1 million volts, so lots of power is possible, as long as you don't mind the brownouts.
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.