I did mention Defense and other science projects. 2 things that are mostly publically funded, although morally I don't see where the difference lies. If you believe in a kind of Peter Singer redistribution of wealth then why stop at public money.

But I'm willing to bet that if SpaceX or whoever ever do become fully self-sustaining, a large proportion of people will continue to view space technology as frivolous and unnecessary toys for rich people, instead of valuable research and development that helps everyone.

I agree generally (when the two are entirely separated), however on the actual context the interesting thing about so much taxpayer subsidization for stadiums in the US, is that it means the entire thing becomes partially taxpayer subsidized including player salaries. The players often can earn so much in part because the stadiums generate so much (varies depending on the league and TV contracts, etc). Taxpayer funds have directly & persistently assisted, decade after decade, in the sports leagues being built up financially. I think cumulatively it is to such an extent that you could never say there is such a thing as wholly private spending in any of the major US sports leagues (I realize this varies country to country).