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

That no central planner can know how much "ought" to be spent on research.

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

I don't know what people would spend their own money on. That's the whole point.

Projects seeming "cool" is a very different claim than political rent-seeking.

Yes, which is why I made distinct points. One is the problem of rent-seeking, but the point you are responding to there is about misallocation.

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.

Oh every group of rent-seekers bleeding the polity dry claim that they've only made a small nick, so there's no need to worry. Meanwhile we die of a thousand cuts. Are academia worse rent-seekers than (say) teachers? Obviously not. But the opportunity cost is probably higher, because they are far more likely to be able to do something productive.