The problem seems to be that this isn't going to be economically viable when you take into account the costs of the research and construction. Take the platinum type metals, which are the most valuable given their mass. Platinum is worth about $30 a gram, so $6 trillion is going to weigh on the order of 200,000 tonnes. The shuttle has the largest payload of any existing spacecraft but even it can only carry 21.3 tonnes of cargo. It costs $300 million just to get the shuttle into geosychronous orbit and it isn't even capable of reaching the asteroid in question. Granted shifting mass down to Earth is cheaper than launching it, but it still has to be encased in a spacecraft unless you want it to arrive as a rain of molten metal across half a continent.
With existing technology you could probably build something more efficient that the shuttle, but even allowing for increasing the payload tenfold you're going to need 1000 flights. To break even you've got to make the flight for $6 billion. Now that sounds fairly feasible with existing technology, but you've got to lift your mining and extraction equipment from Earth. It costs on the order of $25 million to lift a tonne from Earth to geosynchronous orbit, and it'll be a lot more to get it to this asteroid. You've got to lift the spacecraft from Earth each time, for a cost which is probably going to be higher than that of the shuttle. You're going to have to design and build a spacecraft from scratch, since nothing existing is suitable.
The big problem seems to be the huge research and construction costs upfront. On paper if we had a spacecraft with the efficiency and reusability of the shuttle (which is lousy on the former and not great on the latter) capable of reaching this asteroid it might work. I can't see such a craft being developed for less than the cost of the shuttle or Apollo program, which were on the order of $130 billion at current rates. While that still may seem OK given the value of the cargo (and presumably the craft and mining gear could be reused for other less valuable metals), I can't see anyone investing that much upfront on what seems a risky endeavour.
In any case it is simply not economically viable to transport the less valuable metals like iron. It's only worth a few hundred dollars a tonne, so a load of it in the theoretical spacecraft is only worth maybe $100000 compared to a load of platinum at $6 billion. It's irrelevant that there's $8 trillion of it up there as it weighs about 16 billion tonnes. At a very optimistic $5 million a tonne it would cost $80000 trillion to transport it. In space mining only the most valuable materials for their mass can be transported like platinum, gold (maybe) and a few rare things like He-3. I can see the platinum becoming economically viable to mine, but the iron and nickel is far too cheap for it's mass to transport with any conceivable technology. Even if the space elevator lives up to the theory and cuts launch costs by 98% the iron is still not going to be worth shifting. I can't see how we are ever going to be able to mine a tonne of iron in orbit and land it for the $600 it's currently worth when mined on Earth.