The Fed also conducts discount window borrowing. If pure profit maximising were the goal, they might only provide reserves through the discount window. They might even shake down weaker banks.
If confined to buying only Treasury securities, they would just need to maximise the real rate differential between currency and the nominal rate (plus, shrinking their balance sheet so that they no longer need to pay interest on reserves). The maximum level of the real policy rate that is sustainable depends upon your view of the natural rate of interest. If the belief is that the actual real policy rate cannot greatly depart from a natural rate, we would see little difference in policy.
Buying bonds and keeping rates low works to lock in profits once, but the profits will dry up as bonds mature, and are replaced by low-yielding ones.