not sure that helps either as a space elevator concept is useful for cheap and fast transport from earth to near orbit? there are no asteroids in this locality
How about strapping a rocket on an asteroid and pushing it into low earth orbit?
If the space elevator concept stopped at near orbit that would be true. It doesn't. In fact, a near orbit elevator would not even be viable as the counterweight needs to be in geosynchronous orbit just to stay in place. This means payloads can be lifted not only into orbit but set on escape trajectories. This would drop the cost/lb for an extraterrestrial launch from about $10,000/lb to less than $100/lb - making an elevator launch about 1% the cost of a rocket launch. And this figure would actually become smaller per pound as the size of the payload increased - completely opposite of rocket launches.
Once in GSO, the only propellant needed (which can be cheaply lifted as well, removing the limitations on quantity) would be for pushing the payload in the right direction and fine tuning guidance systems.
The return trip of the mined materials would benefit as well. Once mined, a single push would propel the harvested materials into a trajectory that could be intercepted and shipped down the elevator bypassing the need for expensive reentry vessels.