Your numbers only make sense for a single car with no counterweight. For a counterweighted car, you only need to cover the friction losses, and accellerate the payload itself out of Earth's gravity well. The car could be quite massive (within the limits of the carrying capacity of the cable, of course. So thousands of square metres of solar panel are easy to carry in the exo-atmospheric section.

One would stage from one lift to another every few hundred or thousand km to avoid any one counterweighted elevator being too heavy because of too much local cable. In fact, with good design, one can keep the same elevator car and simply swap from cable loop to cable loop, thus swinging up the main tether arm-over-arm. You could swap with downcoming cars in the same way that canal barges can go up and down the same set of locks, so long as there are passing spaces.

For the atmospheric section, you would need more compact and aerodynamic elevator cars, but here you could use physical wires to transmit power a few hundred km from the ground, or augment it by solar power or energy beams, or just accept a slow first day's climb out of the atmosphere. You have no radiation risk here so it doesn't have to be quick.

If you have a pressing need for a rapid ascent for a manned capsule, then you rig the counterbalances. You pre-load excess mass up the cable to make each counterwight heavier than it needs to be. You can do this slowly with low power density over a period of time. Then, when all is ready, you attach the car at the base and it gets accelerated up the cable by each falling mass. There are some inefficiencies here so you don't want to do it all the time, but one could accelerate up the cable at 0.5g relative to earth (1.5g perceived acceleration within the capsule) to the turnaround point, then effectively freefall up to orbit.*

*There are serious dynamical issues with coriolis force, however, if objects move rapidly up and down the cable. This is a second-order effect, but since the cable is arbitrarily thin and has zero lateral strength, it becomes a major engineering constraint. Again, this can be partly addressed by allowing the nominally vertical tether to start-off with a sideways lean that will pull the cargo forward in its orbit and accelerate it to meet the docking ring at GEO.

Between launches, the docking ring will have been slowed and will lag in its orbit until the leaning cables pull it back to speed (or in fact, overdo the job in simple harmonic motion and return the launch tether to its forward angle)