The Fed cannot buy bonds on the primary market, only in the secondary market. That really doesn't matter though, as it shares a balance sheet with Treasury. It will always be the gorilla in the room and sets the rate of return wherever it wishes it to be.

Buyers in the primary market are contracted to purchase all bond issues at a specified rate below the overnight rate set by the Fed. Since they also receive the initial spending deposits they can always purchase whatever bonds are issued from their reserves as a pass through.