Except when they have to compete for high value professors [0].

[0]: https://news.ycombinator.com/item?id=15600275

I'm not sure of how universities are funded in other countries. If for example the government says they will provide a fixed amount per student (yearly adjusted for inflation, etc) that might be a good example of price control. Another thing is many university administrative staff are used to paying themselves outrageous salaries and pensions and they just feeds into the rising costs.

The universities are not really independent from the government: the state runs the university, its faculty and employees are civil servants, etc.

Edit: I was thinking about private universities in the US, it’s true that public universities are already controlled by the same govermnents who pays most of their costs.