Is anyone interested in a stepped space elevator?

Has anyone considered what I am terming a stepped space elevator? It seems to circumvent the current problems related to the space elevator.

Instead of a single tether (like an express elevator that only runs from the ground floor to the upper floors of a building), what is the problem with stopping at an intermediate platform or platforms? The platforms act as huge airfoils/kites and steps so that the tether doesn't need to support its full weight at any point. It does need to be strong enough to anchor the kites.

As kites get higher, there is less air to provide lift, but this is also offset by less gravity to overcome. At the point where there is not enough atmosphere to provide lift, hopefully there is minimal gravity so that the tether can support its own weight at this point to extend into space.

A possible assist to forward motion could be provided by solar panels to power electric drive motors, lessening the tension on the anchor tether.

If the rotational speed of the Earth is too fast, one could position the ground anchor neare the poles (which would also increase sun exposure.) Another possibilty would be to not anchor the tether to the Earth, but this would require the platforms to be powered and/or lighter than air (or only as heavy as the propulsion could keep airborn. Then the lowest platform would act as a small landing pad/strip for cargo to be transferred to airplanes/helicopters as the Earth passed beneath it. Or from a ground perspective, the platform passed overhead. This raises the possible problem of political permission to use airspace, but hopefully the having access to the elevator would be incentive to allow it.

Does this make any sense? Am I missing something obvious?