Eg. For pool does the more dextrous hand need to push the cue or does it line up and guide the front of the cue? I can see tradeoffs each way and the front hand is certainly not just limp when playing.
Hockey is similar. The top or the bottom hand being the more dextrous probably has tradeoffs but I don’t see either grip as being more or less natural for handedness. I don’t play hockey but play golf and cricket which have similar grips and am similar there to you too.
In golf, strength is overrated until you get to the pros.
It has the most degrees of freedom, and more motion. The one in front has a whole table for stability.
But that's just like my opinion, man.