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Variable pitch props are useful for other design conditions. The prop RPM is typically limited to a speed that prevents the prop tip from reaching supersonic speeds, for noise certification. On fixed-pitch props at this fixed RPM, there's a tradeoff between climb and cruise performance, because these operate at two very different advance ratios. Constant-speed props allow the blade to adjust some of this difference.

There's also the engine-out design case, it's much easier to add prop feathering than add more power to the operating engines.

This design doesn't make a lot of sense, the props are located at literally the maximum arm from centerline, which requires bigger control surfaces for engine-out design (heavier and more drag) and gives very little ground clearance in crosswind landings. On the economics side, fuel costs are a small part of operating light turboprops/jets. The biggest costs are airplane depreciation/capital and crew. The real breakthrough would be an autonomous turbine plane that could eliminate crew cost and achieve 2000 hours/year utilization (versus ~200 for some privately-owned jets).