Then University fees are fine then, right? And if the powers that be want to earn £500k, or a cool £1million, then that's also ok, because there's always students with deeper pockets, right? After all, if you stick two people in a room with a tiger, it'll eat twice as much - after all, it's what they do...
I think a university will work towards its own interests and pay to attract the staff they believe they need to do it. So, if a university thinks having a Labour peer on board means they'll have better political traction when discussing how much public payment they get, they'll employ one. It's the same as a bank employing non-executive director who used to be a Conservative chancellor. Both are examples of an organisation acting in its own interests within the rules and business climate they operate under.
If a university can make more money by finding more foreign students that deliver them more revenue, then yes - they will attract them and "eat double". Their goal is to educate as many people as they can without losing money. It isn't to make a profit or pay a shareholder dividend.
My personal goal would be to have universities that work for British students. I would revert to a system where British students didn't pay fees directly. That might mean controlling what courses did or did not warrant getting a grant. That might cause universities to reconsider what courses they offered. As the government could regulate university salaries if it wanted to, but (for the reason I gave earlier) may well be the recipient of one of those salaries in the future - well, I wouldn't hold my breath.