the primary reason for any observed change in MP when cycling between normal and alternate air is........the change in air pressure delivered to the carb resulting from the difference in those two induction paths.
I see it differently:
The "pressure" being measured by the MP gauge is below atmospheric. So, yes, a change in induction air route could have a minor effect, or a major effect, if the air filter is blocked (which I have had with sudden freezing rain). Assuming that the air filter is not blocked, there is very little pressure drop across the filter (or it's really poorly designed). Similarly, there is no (well, shouldn't be) obstruction in the alternate air path, particularly as there is no filter at all. So, again, no pressure drop. However the heated carb heat hot air is much less dense. The MP gauge is not measuring that density, but it is measuring the engine performance running on the air at the actual density. Less dense air, less performance.
My most extreme example of this was a Cessna 185 I test flew with a normally aspirated, carburetted engine, running on Mogas. I climbed it to 20,800 feet, just to see how high it would go on Mogas - that high. While up there, full open throttle (carb heat cold) was around 13" MP, at 75MPH, with the stall warning horn screaming - less dense air.
The MP is neither a direct indication of torque nor is it the only indirect indication of torque.
I agree that MP is not an absolute means of measuring torque, but it's as close a GA plane needs. Note that the Cessna performance charts present RPM, MP, and %BHP in relation. In a given row, the RPM is defined, while the MP and %BHP vary in relation.