Boston University Broad Based Student Debt Forgiveness Discussion

During the last presidential campaign, Mr. Biden promised to enact broad-based student debt forgiveness.   The Biden administration has forgiven student debt for some groups of borrowers (e.g., public servants like police). They reconfirmed intentions to extend debt forgiveness for more borrowers as recently as April 2022.

Suppose the administration forgives up to $10,000 in debt for each borrower with a student loan balance.  Typically, the funds are issued to the lenders who hold these loans, but the money could be paid directly to the borrowers.  If you are a borrower, which payment scheme would you prefer?  From the perspective of the taxpayers who fund this program, does it matter which payment scheme is used?  Please explain your responses.