As a review, the constant-speed propellers on almost all single-engine airplanes are of the non-feathering, oil-pressure-to-increase-pitch design. In this design, increased oil pressure from the propeller governor drives the blade angle towards high pitch, low r.p.m.
NOT AT ALL TRUE. The Hamilton Standard counterweight-type hub - models 2B20, 2D30, 12D40, 3D40 etc. (used on the BT-13, AT-6/SNJ/Texan/Harvard, Lockheed 10 & 12, Beech C-18, DHC-2 & -3, Norseman ...) will slew toward high pitch, low rpm when oil pressure is removed, because of the counterweights. In fact when used (sans governor) as a two-position installation, as on the BT-13 or the original L-10, this was the normal cruise mode - riding the high-pitch stops.
The
Collier Trophy in 1933 went to the inventor of this propeller design.
Early Sensenich props worked the same way. While ferrying a
PA-16 with leaking prop seals, I once intentionally took off in high pitch just to attempt to keep the windshield clean. (light weight, long runway...)