Counterweights and Cables
yes, these disadvantages occur, but the system also allows for rapid ascent of radiation-vulnerable cargoes - i.e. people. A combination of a slow simple elevator for goods and a quick complex one for people would be needed for proper access to space.
The payload is probably less than half of a simple system because you have numerous counterweights, each one of which masses more than the elevator car plus cargo. Nonetheless, the advantages of safe personnel ascent may be worthwhile for less mass penalty than building a radiation-shielded elevator car.