It has often been noted that President Trump holds a vision of his job more befitting a Latin American caudillo than the leader of the world’s oldest democracy. His geopolitical idols trend toward the autocratic — Kim Jong-un, Rodrigo Duterte, Mohammed bin Salman, Recep Tayyip Erdogan, Vladimir Putin. He suffers delusions of grandeur, proclaiming himself “the Chosen One” and having “great and unmatched wisdom.” He accuses those who challenge him of treason, and he regularly wipes his feet on the constitutional principle of checks and balances.

Witness the over-the-top letter his White House counsel, Pat Cipollone, sent House Democrats this week, the gist of which was: Your impeachment investigation is illegitimate, and we will not participate. As if this were the president’s prerogative. Legal experts mostly dismissed the letter as a political stunt. Gregg Nunziata, a former counsel to Senator Marco Rubio, Republican of Florida, called it “bananas.” Walter Shaub, who resigned as head of the Office of Government Ethics in 2017 over the administration’s glaring lack of ethics, said that it “mistakes Trump for a king.”

Fortunately, Mr. Trump’s dreams of dominance tend to bump up against the hard realities of incompetence — his and that of his cronies. It has long been apparent that the president has a peculiar eye for talent. The repercussions of this were on display this week as the Ukraine scandal at the heart of the impeachment inquiry continued to unspool, spotlighting a fresh batch of colorful characters and questionable behavior.

In one of the more bizarre impeachment twists to date, two businessmen involved in the president’s efforts to dig up dirt on former Vice President Joe Biden were arrested on campaign finance violation charges as they were trying to leave the country on Wednesday. Lev Parnas and Igor Fruman are Soviet-born naturalized Americans who have been working closely with Rudy Giuliani, the president’s personal lawyer, to investigate Mr. Biden, one of the president’s chief political rivals, and his son Hunter, who had business dealings in Ukraine. The men were also helping search for evidence to support a (debunked) conspiracy theory blaming Ukraine for the 2016 hacking of the Democratic National Committee.