Due to the large hub of a CPP you do lose thrust as compared to a fixed pitch propellor. So for an ocean going ship a fp prop is better, but for a short sea trader with a lot of docking, such as cross channel ferries and perhaps cruise ships (that are glorified coasters and don't go deep sea as opposed to a passenger liner).
During the 1988 IMareEng IMASS conference on Cruise Ships there was a speaker from KameWa extolling the virtues of CPP, in the Q&A session quite a lively debate ensued, I suppose similar to the sail/steam debate at the time.
It is a case of using the correct prop for the duties of the vessel by lifetime costing of both systems.
Whilst serving my apprenticeship on Hull Fish Dock in 68-73 , I watched the overhaul of CP props and yes there was a darn great spring (similar to those fitted on early B&W exh valve engines about 18"diameter), which put the pitch into ahead in case of hydro-mechanical failure.
The industry was changing from steam sidewinders to diesel and also to diesel Stern Freezers/factory ships which were fitted with the CP prop.
A vessel with a CP prop does require a complicated governor system, a steam recip engine on a tug probably is not fitted with governor, just a hand operated flap valve inthe HP steam line. Though CPP is possible, it is a rather complicated system on a basic engine that requires a lot of hands on to operate.
A tug requiring a high bollard pull needs an efficient prop with a fixed pitch does.
Just to go off topic slightly.
The late United Towing Company from Hull, bought an ocean going tug (Statesman) from the Japanese (I think), built by the US. This had twin CP props(or was it quad) with reduction gearboxes driven by twin v- bank engines (about 18 cylinders per engine). It also had several/countless v- bank diesel alternators. The engines I believe were Detroit Diesels or GM of two different sizes and typical of US thinking more cubic inches the better, hence so many engines. We would have fitted large slow revving 4 strokes not all these little screamers with goodness knows how many units. Cylinder heads were aluminium, though considering the number you would have to hump about just as well.
She was the most powerful tug in the world at the time about 1972. She had good lines and the bridge/ accomodation looked like a liner rather than a boxy tug.
I may have put the thumbnail image up on the tug section, showing her on speed trials in the Humber after her complete overhaul by all the ship repair companies in Hull. We all got a slice of the cake.