1) Pie in the sky research that is beyond the 20 year time horizon of long-view companies and 10 year time horizon of VCs.
2) Research that is amenable to teaching people how to research.
3) Research to advance one's career.
4) Research that is relatively close to Development.
There are overlaps, and it can be hard to differentiate between the types until after the fact, but let's go with this model.
#1 has to be funded federally (i.e. NSF), via philanthropy (i.e. Gates Foundation) or as a monopoly concession (i.e. Bell Labs). This can belong in the University or elsewhere, and may or may not be tied to teaching.
#2 belongs in Universities, as it helps generate the next generation of scholars.
#3 should not be financed by taxpayers. It's also hard to justify this in aggregate coming from tuition. Do we really need more papers on Ancient History, or should we invest the same money in better teaching? I understand you need to be an expert to teach, but it seems like a lot of publishing is purely to generate citations.
#4 If these people can get real world jobs, why not send them to the real world where rather than stay in a profession with very scarce jobs?