So you can increase your input air feed volume while controlling your exhaust.
How can you provide more air feed (initially more O2 rich) in without simultaneously having more air (now CO2 rich due to combustion) exhausting up and out the chimney? And as to retention time within the stove, the volume of flow in/out combined with internal baffle and flow path provided by stove design is the only driver that can dictate that. You can and do intentionally moderate the volume of air flow through the coal bed via either method. Both methods therefore must simultaneously moderate the exhaust. One method maintains the flow of air more uniformly though, and that is the barometric damper. In the end a manual pipe damper moderates draft, but it provides no means by which to uniformly moderate draft fluctuations.
You are dealing with differential pressures. The advantage of the baro is it maintains a constant pressure. So as you open the input side of the airflow, the volume, and velocity of gases flowing through the stove and out the stack, also increase. Now, over a defined range of flow rates, this can be very advantageous allowing a stove to run quite efficiently, at least those stove/chimney systems that run best with a baro.
What will happen however, especially on the side where you are pushing combustion to regions above the "sweet" spot is that you begin dropping more rapidly in overall heating efficiency of the stove compared with running a MPD in that situation.
As you state above, "the volume of flow in/out combined with internal baffle and flow path provided by stove design is the only driver that can dictate that" - but the MPD is part of the internal baffle and flow path of the stove. Hence using an MPD, in fact, you can change this function. This function is set using a baro, and is variable using a MPD.
You also state above, "One method maintains the flow of air more uniformly though, and that is the barometric damper. In the end a manual pipe damper moderates draft, but it provides no means by which to uniformly moderate draft fluctuations." I completely agree with you. However, given the fact that when using my MPD, I typically run with it either closed, or nearly closed, the fluctuation in pressure has essentially no effect on my stove/chimney system as far as fire control or heat output. The driving factor is the limited gas volume allowed to pass the MPD. What I can do, and in fact was doing earlier tonight, was running with my bottom door on my stove wide open, my stove in base burner mode and the MPD 3/4's closed resulting in my stove temperature running around 850F and my chimney temperature running about 255F. You cannot get that kind of temperature differential running a baro. You might get your stove running up around 850F, but your stack temperature will be pushing 400F.
I'll repeat myself for those who feel I somehow fall into one "camp" or the other: the baro and the MPD are functional units of a stove/chimney system, use of one or the other, or combining both together, may provide a particular stove/chimney system to perform optimally.