Re Hamilton Standard CW Propellers as fitted to Harvard,SNJ,

[sprucegoose]

Re Hamilton Standard CW Propellers as fitted to Harvard,SNJ,T6, Model No 12D40-CW

I am looking for an answer as to why these propellers as fitted to single engined aircraft have counterweights? As I understand Constant Speed Propeller systems, On single engined aircraft oil pressure is used to coarsen pitch so that in the event of Governor (CSU) failure the propeller blades under the influence of Centrifugal Twisting Moments will move to fine pitch so that engine power may now be controlled using the Throttle. On Multi engined aircraft this is not a desirable feature as a propeller windmilling in fine pitch produces excessive drag (and therefore yaw), so counterweights were fitted at 90 degrees to blade chord to allow centrifugal force to move the blades to Coarse Pitch ie on the way to feather. My understanding of counterweights is that they are generally only fitted to multi engined aircraft? Why, in the event of CSU oil pressure failure on a single engined aircraft would you want the blades to move to coarse pitch? Am I missing something?? Any advice would be appreciated.