The amount of air/fuel mix that gets into the cylinders is going to determine the power production at any given engine speed. This is going to be dictated by manifold vacuum. If there is zero vacuum in the manifold then the full amount of atmospheric pressure is pushing the air/fuel mix into the cylinders. On the other hand, if the throttles are partially closed and this results in some amount of vacuum in the manifold, then there will be less than the full amount of atmospheric pressure to push the air/fuel mix into the cylinders. Less charge in the cylinders means less power.
I can see where at lower engine speeds, on a lower horsepower engine with a 2X4 system, if both carbs were open all the way on the primaries but the secondaries were still partially closed, there still may be zero vacuum in the manifold, so there would still be maximum cylinder filling. But at higher engine speeds, on a stronger engine, less than full throttle opening is going to give some manifold vacuum, which will reduce power.
Seems like velocity through the carbs will play an important role at low engine speeds also. Let's take the case where the primaries are open but the secondaries are still not in a vacuum secondary carb, and there is still zero manifold vacuum at this point. All the air will go through the primaries, causing a certain amount of fuel to be drawn from the venturis and into the engine. Now, if we tie the secondaries mechanically so that they open as well, velocity through the venturis will be reduced, and we will see less fuel drawn into the intake, resulting in a lean condition. So, if you take your vacuum secondary carb and try to tie the secondaries so that they open mechanically, the engine will be lean and the car will bog at low engine speeds. To me this is a carb problem; mechanical secondaries need more accelerator pump shot to overcome the lean condition. That's why there are double pumper carbs.
On the dyno, accelerator pump shot doesn't enter into the equation, because the whole run is done at wide open throttle. Plus, if you have a lean condition at the starting engine speed, you can jet up to compensate.
For the engines we work on, I don't think it is common to see a partial secondary throttle opening result in zero manifold vacuum at 2500 RPM or higher, even with a 2X4 intake. I'm sure that's why I've seen power increases when tying the secondary throttles open on vacuum secondary carbs.