I'm completely with oggers. To restate from my own words, more succinctly, may add some clarity.
We must differentiate between power input vs. power output. Assuming constant RPM (we're within governing range), the inputs are:
Manifold pressure (Which is itself affected by ambient pressure, throttle, and other obstructions in the flow like filters, different plumbing, etc. in the alternate air path)
Density (temperature)
Spark timing
One vs. two sparks
Mixture
Probably others I'm missing off the cuff
The only result:
Torque
Anything that changes power, obviously changes the result, torque. But we don't have a measure of that. A second best correlation (but not measure) is manifold pressure. Assuming that MP is the only thing that changed, we can use that as a power correlate. However, it is not an indication or measure, because if any if the other inputs changed, that also changes the result, which we have no way of accounting for. For example, we can pull the mixture way over-lean into an obvious power loss (that shows up on the airspeed indicator/VSI) but it won't show up on the manifold pressure. For a stronger example, when we shut down the engine upon parking, the manifold pressure goes to full whereas the power goes to zero! Therefore it's incorrect that "if you do anything which reduces power on the whole, the MP must reduce." The MP is a good-enough power measurement substitute, only if we know nothing else has changed.
(Succinctly, MP affects power, but power doesn't necessarily affect MP.)
For the question of what does carb heat do to MP, this condition (only one variable changed) is not met. With carb heat application, we know the density decreases (duh) but at the same time we change the plumbing which has its own effects, maybe more than one. A filter goes away, which is a gain. But maybe we go through a more circuitous hose route with more bends and an intake location that does not act as ram air, which is a loss. Which predominates? We can't know experimentally without isolating every variable. The only way to really find out, is to change to a carb heat system of (for example) electrical heating pads around the induction that can be switched on and off, so only the presence of heating changes, with no other changes of plumbing. Impractical, but it would be one way to isolate the variable. Maybe there are others?
But as it stands, you can't turn the carb heat on, see the MP change by X, and conclude that that's the result of density.