Except it's so wrong. It has been shown that the government will fund things that corporations won't. Corporations typically will only engage in R & D that has a payoff within a certain amount of time, typically much less than government funded research might yield. This is known, and examples abound.
And here we have new motors, the result of government funded research. Are you saying the motors don't now exist?
When the government does something, you see the thing the government did, and you reason (often correctly) that had the government not done it, it wouldn't have been done. However, what you don't see is what those resources could have produced had they not been taken by the government. And what you fail to factor in is the cost of all the research that doesn't produce useful results.
Yes, you need the government to take risks so bad that nobody's willing to take them with their own money. But it stands to reason that the vast majority of the time, the costs outweigh the probable benefits. We'd be better off without it.
Had the government not taxed the wealth that funded that research, those who produced that wealth would have used it for things they value more.
Sure, Opportunity Cost 101. But not everything is measurable in money. What about sentimental things like health, education, or family? How much money is your health worth if you lose it? $1000? What if you can afford a million dollars - does that make your health
worth more? It doesn't make any sense to apply cold-blooded market efficiency to certain things. Otherwise one ends up going down a slippery slope towards analysing the financial pros-and-cons of things like euthanasia and eugenics.
I agree that in many cases government research may be a waste of time. If people are allocated a budget, they better use it or they'll lose it!

However, my point gains the most significance in cases where there are clear moral values at stake, yet its worth is not measurable in money. E.g.: cancer cures, search-and-rescue/disaster relief tools, plentiful sources of potable water.... Even loss-making space exploration has value.
Health will be redefined to mean something else, education will be redefined to mean something else, family will be redefined to mean something else... all in pursuit of tricking people to maintain funding. You won't see a cancer cure in the near future because the majority of the research focuses on one target, then trying to compensate for everything else that fucks up in the system, etc. This is what occurs when linear thinking is used to assess systems with multiple feedbacks. Once people start really trying to model these tissues as systems they will then have to waste a bunch of time on getting rid of all the false interactions from their models and basically do the whole thing over again from scratch anyway. Best treatment for cancer is what it has been for 50 years: detect early, cut it out, then, if necessary, poison the person to near death in the hope the cancer dies first.