I think the issue is that many feel public institutions shouldn’t be run like a business in the first place. As an example, if many government services were run with the bottom line as the primary motive, many rural citizens would find they no longer receive those services
If money is involved, it should absolutely be run like a business. But just because it is run like a business doesn't mean the bottom line is the primary motive.
And don't forget that the majority of a universities money is not government money.
Raising $10 million for a stadium is far easier than raising a $10 million endowment for a science lab.
But when alumni come back for the football, you can hit them up for money for the science lab.