CPP is typically used to maintain a constant engine RPM for generators, hydraulic pumps, refridgeration plants, or to improve maneuverability, or in gas turbine and steam powered military ships so that they can avoid a reversing gear.
Also in RORO's where quick acceleration and high cruising speed are needed, icebreakers where you need high thrust for breaking ice and still achieve a high speed in open water.
They are used to give you high thrust when needed without over-revving the engine at high cruising speeds, or to allow you high thrust without overloading a smaller engine.
For the most part diesel engines don't vary in specific fuel consumption between different loads. Obvious at 0% load they are 0% efficient, but the difference in specific fuel consumption between say 30% load and 90% load is less than 10% (for a commercial engine. With that and the fact that a CPP is only optimum at one pitch angle, you erase the benefit of a CPP.
Look at the Caterpillar website for some engines and you see the relative flatness of the specific fuel consumption curves.
You won't often see a CPP on an ocean going crude carrier, even the smaller ones with 25,000HP (well within CPP territory) even though they see wide changes in loads running with or into the wind/sea, and fully loaded or minimum ballast.