1) It's not like the Soviet Union was a terrible hellhole for research. It had impressive research output for decades.
2) That's almost beside the point, however. Let's take it as a given that more good research, whatever that is, is a worthy goal for a society, and that the market under-invests in it in favor of short term profits. It's obviously not a binary of either 100% government funding or 100% private; it's not even really a one-dimensional continuum, because for the large capital expenditures typically involved in research, the government always has a heavy involvement, either in tax breaks or grants or collaboration. The question is, how do we allocate money to produce the best research? It's undoubtedly at some value that's somewhere between 0% and 100%.
3) There's a whole lot of money floating around now that makes endeavors like SpaceX practicable. That wasn't the case in, say, the Sixties. Even if the arguments for government spending on research were weak now, they'd be stronger in the 1960's, particularly for things like space exploration that required substantial concentrations of capital.