I think currently the Fed load some of the printed money to the banks with prime rate, which means Fed is making money as well. On the other hand, the Treasury issues bonds. It seems to me the Bond rate is higher than primpary rate because there is so-called I-bond. Why don't the Fed simply gives money to the Treasurey to eliminate debt.
Another immature idea about Fed and Treasurey: US debt is $7Trillion, while US annual economy is $10T, plus many foreign countries hold a lot of US$ (I am not sure how much). $7T compared to the total dollars in circulation should be small(let's 10% of the total). Why don't the FED just print $7T, give it all to the Treasury dept and let them pay off the national debt. Of course, dollar will become cheaper with higher inflation, but the debt is gone. And foreign countries like China's dollars are depreciated, ie, China helps pay US national debt.