The only thing that makes Carson's appointment ironic is the editorial lenses through which you view it. Was it ironic that Obama was elected to lead a country that he promised to radically transform; a country that he spent much of his presidency trashing? Was it ironic that, as the chief law enforcement officer of the country he has run roughshod over the rule of law? 

Obama's contempt for the sources of American greatness was tragic. But it wasn't ironic. It was very consistent with the ideological filters through which he viewed American history and Western civilization. 

By your reasoning, Monte, Tom Price and Scott Pruitt are also ironic picks for their positions to lead HHS and EPA. It seems to me that you perhaps need to depoliticize your understanding of irony. It would certainly have been highly ironic for President Obama to appoint Scott Pruitt to head the EPA. And it most definitely would have been the height of irony for Trump to appoint Al Gore to head the EPA.