This is absolutely idiotic on the surface.
There’s probably a hidden agenda as to why they are doing it this way.

Fannie/Freddie do not own these loans, they guarantee them.
Mortgage backed securities (such as GNMA’s) were sold that hold these loans.

The sensible plan would be to sell bonds at today’s rates
and pay off the existing bond holders, leaving the principal balances the same but lowering the interest rate to the homeowner.

Many of these existing loans from 10 years ago could be at 6%-8%.
Lowering rates to <4% would drop payments substantially with no need for reduction in principal.
Most people dont care how much they owe. If their payment dropped 25%-50% most people aren't going to default.

The net result is that Fannie/Freddie would still be on the hook for the same amount and any losses and it makes more sense than writing down principal to people who haven't paid.

The bondholders will receive their money. The reduction will come from Fannie/Freddie. It doesn't make sense.

(I don't know if Fannie/Freddie pay taxes on their profits but if they do, any losses would offset their profits and lessen their tax liability)