Finally! Gawd! Yes? Why did I not just speak in watts? Possibly because the OP sounded a little less up to speed on the whole concept?
My point: almost every time I have put a sub in a garage for a home handyman or hero gear head, and I tell him a 30 amp (or 50) is going to serve his demands, he wants to challenge me until I explain that he actually has two legs of power at 30 or 50 amps in a three wire circuit, not one, as might at first blush appear to be the point.
I find myself complicating issues sometimes simply due to the fact that I stand in the classroom.
When I teach a class on transformers, which is where we are at now, and how they relate to a dwelling unit service we discuss 120 verses 240 volts that is supplied by the transformer.
I present the question to the class which is correct for a 200 amp service; the service will be 200 amps or 400 amps if the two legs are added together. Most answer that it would be 400 amps if added together which is incorrect.
The most 120 volts that can be achieved would be 200 amps. When the second leg is added to it the addition would be +200 added to -200 or if both legs were loaded to the max there would be no 120 being used at all. When we load one side to 10 amps and then the other side to 5 amps even if what are used are 120 volt appliances then the service will only see 5 amps at 120 and 5 amps at 240.
After going back and reading your post I see that what you were saying is that if each 120 volt appliance being used at one time that the total draw on the feeders would be just that and you did not say that each leg would be carrying twice the rating of the conductors or breaker. As a matter of fact you were only addressing each branch circuit instead of the total amperage being on the feeder.
My mind went to the load on the neutral which I guess was easy to see and how that any balanced portion of the 240 volt feeder would be a series 240 volt circuit instead of the parallel 120 volt circuit as you were addressing.
I am slow but I usually get there.