The fault in your logic lies at "once this becomes obviously economically viable". If and when it becomes economically viable. And even if there is "asteroid mining" during his lifetime, what makes you think that it'll be a manned mission?
NASA's space program has nothing to do with profit, it has to do with knowledge. And that can never be replaced by private companies.
NASA's role isn't flying billionaires around planets for profit. That can happen through private companies just like its happening with planes now. Knowledge and exploration is NASA's game. No private company cares for those, so funding will come by the state. Its more effective then to fund NASA, than some private company that stands to make profit by doing it.
The error in your logic is the casual assumption that knowledge can not be profitable. Hopefully the mere act of stating it is enough to show how untrue that is? And that's why there were private discovery expeditions, per WalterBright's point.
NASA's space program has nothing to do with profit, it has to do with knowledge. And that can never be replaced by private companies.