I'm not counting electrons twice. Neither is Bud. I take 200 amps worth of 120Volt eqpt and plug it into outlets that are driven off of one hot leg of the 240Volt 200 amp service. I take 200 amps worth of 120volt eqpt and plug it into outlets that are driven off the second hot leg. I am now supporting 400 amps of 120volt loads. It doesn't get any more basic than that. I agree the current is flowing in series and is actually a 240Volt total load and the service is running 200 amps. That is what I have been saying all along when others were saying that you have conductors in parallel, a second conductor carrying more current, etc. But from any reasonable perspective, if I can plug 400 amps worth of 120volt eqpt into the house, then I am in fact driving those loads.
If the homeowner asked you how many amps worth of 120Volt eqpt is the max that the 200 amp service can support, what would your answer be?