Yeah, as I said, I think funding research is one of the least wasteful things states do. But whatever small gains they stimulate pales next to the all the other opportunity costs they incur. All taxation is by definition a slow on economic growth and entrepreneurship within an economy, because it takes money from the most-valued use (where people want to spend or invest it) and puts it into less-valued uses (where the government wants to spend it + interest on government debt). Even if you accept the notion that taxes are the price we pay for a civilized society (and this is an acceptable position), the "price" is a massive opportunity cost.

So I could take one of two positions. I could say that yes, you're right that government research grants do a lot of good, but all of the other ways that governments stifle innovation have negative 20 times the magnitude of effect as the government research money's positive effect. But I would even go so far as to say that the state money to research itself is worse than if it weren't taken out of individuals' and businesses' coffers to begin with.

It seems like you can divide government efforts at research development into two categories, big state agencies and projects like NASA or individual handouts like genius grants and the like. NASA did lead to some innovation, but I think its pretty safe to say it was a massive failure from a cost-benefit standpoint. The space shuttle program cost 200 billion dollars over just 30 years, and led to a couple of dozen deaths. Were microwave ovens and remote controls emerging a few years before their time worth these costs? Maybe and maybe not. Would an extra 200 billion dollars in the pockets of individuals have stimulated some innovation and entrepreneurship in its own right? Definitely.

As far as government grants to individuals for research, these are possibly less wasteful and more beneficial than big projects like NASA, but the big problem with these is rent-seeking. I'll just leave this short video to explain how costly it is to give away money to people.