Actually, there are knock down targets I've encountered that would be left standing by a .410. There were some tall plates, with their backs to a strong wind, at the Washington State blackpowder shoot last April. Some folks had trouble taking them down with 12 gauges, as the wind would reset them before they fell, and the stage directions said to make them fall. A kid in the buckaroo class would only have to hit the target, in that situation, so the .410 is no handicap.
There are minimum bore diameters for all cowboy action guns, and for adults, the shotgun minimum happens to be set at 20 gauge. I guess that's to make the shooting a little more "true" to the time and to the spirit of the game.