By comparison, there's $956 quintillion of platinum in the earth's crust, and similar amounts of other precious metals. 5 ug/kg (incidence of platinum in crust) x 6x10^24 kg (crust size) x 32 USD/g (price of platinum) Asteroid mining is crazy silly. We're not supply limited for any element on earth, we're demand limited. If the price of platinum rose substantially, so would supply. It doesn't matter how much of anyth…
Additionally, the production cost of most rare metals is very highly correlated with the cost of energy. It seems likely that space mining may have to compete with metals produced at a price an order of magnitude cheaper than the current price because cheap solar energy appears to be coming.
For instance, it'd be practical to build a multi-kilometer diameter mirror out of thin plastic, and just melt the entire asteroid and distill off what you wanted.
To expand a bit: a mirror for a solar furnace on Earth has to be strong enough to hold itself up against the force of gravity and handle wind and precipitation loading. A mirror in space doesn't. It can be one molecule of plastic thick, with a few atoms of thickness of aluminum as a coating.
Plus you don't have to worry about cleaning off dust, bird poop, and whatnot.
You're going to need some station-keeping so a large, flimsy mirror doesn't drift with the solar wind, but even the purest asteroid is going to have some slag that will make dandy propellant.