I get the gist of your argument, at least as it applies to sattelites. In the case of a space elevator, however, there IS a source of energy available - the angular momentum of the earth's rotation, transferred through the cable attached to the earth.
the angular momentum wouldn't be making this a vertical trip and eventually, the rotation would cause the whole thing to wrap around the earth... Again, theory and fantasy, not practical or possible. Ever seen a spinning galaxy, think of the arms.... this would be the effect.