There are so many problems.
1. The asteroids are not near earth. Occasionally one ventures nearish, but at tremendious velocity.
2. The delta-m required to bring even a small asteroid into earth orbit is tremendous.
3. Any large, steerable body in orbit or above is potentially a hyperweapon. That is, the type of thing that makes regular WMDs look like toys. The last time a major body impacted, there were dinosaurs roaming the earth. There aren't any more. Do you want to see that in the hands of private industry?
4. No-one has the faintest idea how to do zero-G refining, with only energy as an input.
5. Most asteroids, and all comets, are crap-grade ore.
6. The only way it might be at all economical would be to keep the minerals in space, and use for space-based manufacturing of more ships - there's no point bringing most of them down, as only a few minerals (Platinum, gold) are expensive enough to justify the reentry cost. So you'd be mining minerals for an industry that doesn't exist.
It's a nice idea, but what we have here is the basic chicken and egg situation. For space industry like this to be practical requires great advances in very specific fields of technology that aren't going to advance without space industry, and a space economy to purchase the goods which can't take form until there is an established industry beyond geostationary orbit. Asteroid mining remains a pipe dream unless either someone makes a breakthrough in technology (perhaps a space elevator) or else many trillions (Yes, with a T) of dollars are thrown away on mega-projects in the hope of maybe setting up favorable economic conditions for someone else to profit from.