If you read my earlier long post carefully, you'd find that I have the gear ratio K in all my calculations. The conclusion is that acceleration is only determined by the (entire) torque curve and gear ratios, not power.
Here's where a concept difference likely caused confusion for you and ifidonlike:
It's true that:
Higher Power => Higher rate of change for Kinetic Energy.
Here, I'll accept your assumption of no frictional loss, and I'll even give you no air resistance.
But, Kinetic Energy is not itself Velocity. Velocity is the square-root of Kinetic Energy. NOW:
Higher rate of change for Kinetic Energy ==XXX=> Higher rate of change for its square-root (or Velocity).
This is Calculus 101. The rate of change for Velocity, is of course Acceleration, as defined in Physics 101.
In fact, take any engine and consider acceleration in gear from the torque-peak rpm up to the hp-peak rpm. During this stretch, power keeps increasing, but torque delivered at the wheels, hence acceleration, keeps decreasing.