When you press the gas pedal in your car down (which used to just be a cable to the throttle body), does your car instantaneously increase in speed to match the pedal position?

All you're doing is letting more air in - the RPM is a function of the power the engine generates; more fuel and air than is currently needed for the current load at the current speed = increasing RPMs.

If you put the clutch in, a little blip of the gas is all that's needed to get the RPM quite high very quickly. The moment there's load on there, the same blip will not do very much at all.