Velocity is an output, not an input.
If I managed to follow along correctly, I agree...lol
In terms of the player swinging the cue. Velocity is indeed the result of the energy applied to the mass of the cue. Lower the mass, maintain the energy, the end result (velocity) is greater.
The portion of the break I tend to focus on, is the transfer of energy to the cue ball from the cue. This requires velocity. Infinite kinetic energy at near zero velocity imparts near zero velocity to the cue ball. We could add coil/spring action of the compressing cue tip or whatever if we would like to complicate it further, but generally speaking you cannot generate greater velocity on the cue ball than what the cue spd was.
Additional pool cue mass (kinetic energy) only matters if the player stops applying energy to the forward motion of the cue at the moment of contact. However that is never the case, and I'd wager that nearly all additional losses the lighter cue suffers from the lesser amount of kinetic energy are compensated for by the continued motion (energy) of the player.
I respect your physics/mechanics expertise,
Ok cool.... I'm assuming your comment means he has some higher education working for him. Based on his posts, I figured he had to be someone with a severely greater knowledge of physics then myself....