How does having a huge debt allow you to charge a higher fee?
Doesn’t a debt weaken your negotiating position - you have less freedom to walk away for example because you need to service your debt.
It doesn’t work that you can charge a higher fee just because you plead ‘but I have a debt!’
See also: high prices in destination shopping. The landlord sets the rent and all stores have to pay the rent, so all stores will have the same high prices no matter how stiff the competition between them.
They’re able to due to restricted supply.
Medical schools charge students a lot because doctors get paid a lot, and doctors have to be getting paid a lot to justify the enormous debts medical schools leave them with. It's a vicious circle that will never end without serious government intervention.