Couple of points about CS props in an attempt to simplify things, excuse me if I repeat something already said.
The reason that CS props give better efficiency than fixed pitch or variable speed props is that they allow the blades to work at their optimum angle of attack (about 4 degrees) over a wide airspeed range.
The angle of attack of a fixed-pitch prop is of course greatly affected by the forward airspeed of the aircraft and its pitch angle is by definition a compromise of design. A fine pitch angle is needed for low IAS and a coarse pitch for high IAS. A fine pitch prop will give good initial acceleration and climb but is no good for economical high speed cruise. Conversely, a coarse pitch prop is no good for acceleration and climb but gives a good cruise performance.
This is reputedly one reason why the early Schneider (high speed) Trophy aircraft were seaplanes. This was before the days of the CS prop. These aircraft needed a very coarse prop setting to get to the high IASs required to win the prize which meant at low speeds the prop was very inefficient. The aircraft accelerated poorly from rest and consequently needed a very long takeoff run. As airfields were quite small in those days, a water takeoff offered a greater distance.
The reason for the rule "rev up / throttle back" is to prevent mixture detonation caused by so-called "overboosting", or too much MAP (too much mixture charge allowed into the cylinders) at too small an engine RPM. Detonation will of course cause piston damage and possible engine mechanical failure in a short time. How much MAP the engine can stand at any given RPM depends on its individual characteristics so the POH certainly is the only authoritative advice to follow.
Hope this helps.
