You both raise a valid point. About the only possible answer I can imagine is oddly enough, the US House of Representatives and the US Senate.
Constitutionally, the power of impeachment has been limited almost exclusively to corrupt federal judges. However, one time in the past, congress did impeach a cabinet officer, William W. Belknap, president Grant’s Secretary of War. He resigned before his senate trial, yet was acquitted by them.
The Constitution grants the House the power to impeach “The President, the Vice President, and all civil Officers of the United States.”
So all it takes is the political will of a majority of congress, but unfortunately 2/3rds of a majority of the senate, to turn such scoundrels out of office.
In practical terms, the senate does not wish to convict those other than federal judges, because the house is willing to impeach them, and forward the impeachment to the senate.
So what needs to happen is for the house to make it a more common practice to impeach evil and corrupt bureaucrats.
This would be a huge vitamin shot to the power of congress, and would do much to rebalance their branch against the “imperial presidents”.
Eventually even the senate would start to convict the worst of the scoundrels, and it would become a more relaxed process, with the senate willing to do so.