The upper end of a space elevator is moving considerably faster than orbital speed at that distance from Earth. As a result anything released from the top of elevator would get thrown away from the Earth instead of just entering into high Earth orbit. How much would being released from the end of a space elevator at twice geosynchronous radius reduce travel times or the amount of rocket thrust needed during Earth departure for interplanetary probes.
I'm assuming the cable is capable of damping out the oscillations caused by releasing the payload. Doing so is necessary to release a payload at any altitude other than geosynchronous altitude; due to the amount of activity currently occurring at significantly lower altitudes being able to do so seems to be a necessary requirement for constructing an elevator in the first place.