Asteroid mining would be so time, resource and financially consuming that is seems a waste compared with terrestrial solutions to this resource crisis. Why go to the trouble of building this non-existant technology, and travel unthinkable distances, when cheaper more realistic technology could be looked in to in order to recycle these resources more effectively. Recycling of precious materials we have already mined, put to use and then discarded on a massive scale, would be much less wasteful and a much better outlook to adopt, moving forward.
Biohydrometallurgy is one method proposed, where microorganisms are used to react with and therefore extract precious metal particles from waste water and industrial sludge. Many new forms of technology, specifically biotechnology, require mainly processes and materials that we already have, are commonly used, or that are biologically occurring naturally. The only viable future for the human race on this planet is a sustainable one, and being better recyclers, just like Mother Earth, is the best method for that.