Tyson is wrong in his belief that free market capitalism abhors risky investments. On the contrary, the free market scenario minimizes risk for any investment, simply by ensuring government will not interfere and change the rulebook during halftime. Sure, there are substantial risks in space travel. But as has been discussed at length in these comments already, risk is only one-third of the equation:
Payoff = (1 - Risk) x Reward + Risk x Loss
There is no way to dismiss an investment purely on risk. If the Reward and the Loss are in alignment, any risk can possibly be worth it. Heck, what if the lottery was free to play - what idiot wouldn't play each week?
To be blunt, there are terrestrial ventures that seem riskier than space mining. Heck, look at Afghanistan. That country isn't poor - its filthy rich. There are over $1 trillion in minerals beneath the feet of those backwards Pashtuns. Their mineral wealth could pave their streets with gold, send every child to school, modernize (or render extant) their food, health, and transportation sectors.
But it borders on impossible. First, the Taliban have fought the mightiest army in the world to a standstill. Any mining venture would be subjected to relentless and bloody attacks, as well as sabotage. To them, Afghanistan's greatest resource isn't minerals, oil, or anything else earthly - it is Islam. Large-scale mining would need roads to be built pretty much everywhere, since much of the country has none. Despite the enormous benefits mining could bring to their country, Afghanistan has a corrupt government, riven by tribal and family squabbles. Much like Africa and Iran, it is not difficult to foresee corruption leading to a small number of connected tribesmen becoming multi-billionaires, while the rest of the country wears sandals.
Space mining at least doesn't require miners to duke it out with decapitation-happy, Third-world savages.
Another argument against Tyson's claim is that, quite simply, we do not practice free market capitalism in America (nearly any Western country) anymore. We practice crony capitalism, where huge swaths of production are controlled of a few powerful men, with loyal (or, if nothing else, frightened) men filling legislatures and working on their behalf. Instead of focusing on improving the productivity of their industries, their main pursuit becomes rent-seeking. Regulations are applied stringently to those outside of the inner circle, to raise the barrier-to-entry. Inside players are allowed to skate.
Here is a general, dismal scenario:
1. Some company shoulders enormous financial risk at developing space technologies.
2. After much hardship, this company actually pulls it off, e.g. a working mining pipeline from the Moon or Mars.
3. Stakeholders in the current economic landscape view this activity as a threat, and dispatch their political Sardaukar.
3. Laws are passed plunder the company, and/or take over administration of their operations.
One can easily envision some slimy future President lecturing the American public on how regulation of space mining is necessary to prevent the sale of yellowcake to terrorists.