At this point I think I have to cite Use of Knowledge in Society, Hayek, 194

Sorry, I'm not following. You are citing Hayek to argue what here?

Sure. How much? Where I live, we spend approx $4bn per year (0.64% of GDP) on state-funded research (note that this figure is conservative because it doesn't include the way that higher education funds get siphoned off into research). Conservatively then, let's say $1bn in deadweight loss annually, just in this country - and our state-funded research is low compared to most OECD countries. If we extrapolate this figure to the world economy, we get a deadweight loss of approx $127bn annually, just due to government research spending. That's a lot of bednets.

Ok. So we have less than 1% of GDP going to state-funded research. And where is that going to go?

I am talking about money being spent on worthless projects because they seem cool or win votes. NASA has a budget of almost $18bn!

Projects seeming "cool" is a very different claim than political rent-seeking. In this case though, looking at the overall NASA budget isn't very helpful: First, much of that budget is not going to what would be considered academic research. Second, you are talking about the space program of one of the world's largest economies, so the total cost is a misleading metric. Third, technologies developed by the US space program (especially GPS, communication satellites and weather satellites) have had large-scale world-changing impact.

Of course it's a serious argument - subsidizing one group of rent-seekers encourages others.

It often doesn't, and the case you've picked is a really good one. In the US, many of the people getting farm subsidies are people who are rural and if anything anti-ivory tower. A large fraction would probably be turned off of the idea of government subsidies if it was compared to what those East Coast intellectuals were doing. (I'm engaging in some broad brush strokes here obviously but some people like this do exist.) This sort of thing is connected to why many groups (including farmers) have tried to get their money through tax breaks rather than direct subsidies. Of course, from an economic perspective, tax expenditures are identical to subsidies. But people don't like to think of themselves as getting handouts so they prefer tax breaks (at least in the US).

By the way, my point earlier about only a small fraction of tax money going to academic research was (to be clear) about the claim that academic research would necessitate tax policy watchdog groups.