Nope, asteroid mining will not solve that issue - the issue is kickstarting it, expending the energy to actually get the necessary mining and refining gear up there in the first place. To get all the minerals out of the ore and to refine it into high quality metals, build the necessary alloys and cast them under microgravity will make it necessary to lift hundreds of thousands of tons of stuff up there. Not to mention that most of our refining techniques, e.g. floatation, will not work in microgravity, so completely new ones will have to be designed. At the moment the startup costs kill the whole endeavour. We need cheaper lifting capacity first. Orders of magnitude cheaper. That's what we have to research before producing vaporware by tagging asteroids.