Going back to the laws of physics, it's been said already that this is about how energy is used. Throttle brings more energy into the system, which we can (using the control surfaces) deploy to accelerate or gain height. It converts the chemical energy of fuel into kinetic energy (and/or potential energy if you climb) and mostly you dont notice any immediate consequence of losing the chemical energy. The elevator can convert potential energy into
kinetic energy or vice versa, but then you do notice the loss of the other energy type. Use the elevator to convert kinetic energy into potential energy (climb) and you will notice that the loss of kinetic energy results in deceleration. Using elevator and throttle allows you to do both at the same time.
Ok, so it's been a while since I was at school so maybe someone will re-educate me at this point.