This might help on some of the points in this thread:
https://thecollegeinvestor.com/39673...student-loans/
I think the discount rate in these analyses is too low (meaning the cost of the program is higher and it is a net loss - or net subsidy) because of the credit risk. But taking the article as it is, I would note that no federal loan programs that I’m familiar with use the term “profit”. I’ve only ever seen “negative subsidy” which implies that the administering department (education in this case) could reduce its share of the federal budget or push some funds to another department.
Also worth noting is the Treasury is the lender, not the dept of Education. This is typical with most (all?) federal lending programs. Grants come from the departments issuing them, and are in their federal budget allocation. Student loan forgiveness administratively is an increase in Ed’s budget being used to pay the Treasury back for the loan.