Thoughts:
Barr knew he would not accept another position, that he's a jackass and would go out the hard way. So by offering it, Barr immediately looks better and shows the derp for the derpmaggot that he is.
Trump is no one's fool. If he wanted this guy in that position, he had a good reason for it. If it was merely a mistake, he would have been removed quite some time ago.
Chum - leaving him in place for a while would garner evidence about his wrongdoing and those handling him.
Mark
Mark