Power determines both height and speed as there are any number of combinations one can get for a particular power setting.
Examples....Full RPM....flat Pitch...minimum power...Zero airspeed....either sat on the helipad or in autorotation with Vne on the clock.
MCP....Max attainable height....low speed.....50 feet AGL...high speed.
MCP...2000 feet.....some speed....to go faster....nose down....but lower altitude for the new speed.....slow down to original speed (nose up) more height.
So I say all you CFS guys are wrong.....it is Power that matters and what you do with it.
Cyclic controls the pitch and roll attitude of the aircraft, Collective controls Power.
In Hover....Collective controls Power which determines Height.
In Forward flight....Collective controls power which provides Speed/Height.