One of President Trump’s rare strengths has been his ability to project competence. The Dow Jones stock index is up an astonishing 2,200 points since his election in part because investors believed Trump could deliver tax reform and infrastructure spending.

Think again!

The Trump administration is increasingly showing itself to be breathtakingly incompetent, and that’s the real lesson of the collapse of the G.O.P. health care bill. The administration proved unable to organize its way out of a paper bag: After seven years of Republicans’ publicly loathing Obamacare, their repeal-replace bill failed after 18 days.

Politics sometimes rewards braggarts, and Trump is a world-class boaster. He promised a health care plan that would be “unbelievable,” “beautiful,” “terrific,” “less expensive and much better,” “insurance for everybody.” But he’s abysmal at delivering — because the basic truth is that he’s an effective politician who’s utterly incompetent at governing.

It’s sometimes said that politicians campaign in poetry and govern in prose. Trump campaigns in braggadocio and governs in bombast.

Whatever one thinks of Trump’s merits, this competence gap raises profound questions about our national direction. If the administration can’t repeal Obamacare — or manage friendly relations with allies like Mexico or Australia — how will it possibly accomplish something complicated like tax reform? Failure and weakness also build on themselves, and the health care debacle will make it more difficult for Trump to get his way with Congress on other issues. As people recognize that the emperor is wearing no clothes, that perception of weakness will spiral.

One of the underlying problems is Trump’s penchant for personnel choices that are bafflingly bad or ethically challenged or both. Mike Flynn was perhaps the best-known example.

But consider Sebastian Gorka, a counterterrorism adviser to the president. Gorka, who is of Hungarian origin, founded an extremist right-wing party in Hungary in 2007, and The Forward has published articles claiming that Gorka had ties to the anti-Semitic Hungarian right and is a sworn member of a Nazi-allied group in Hungary called Vitezi Rend.

Members of the organization use a lowercase v as a middle initial, and The Forward noted that Gorka has presented his name as Sebastian L.v. Gorka.

Gorka’s background might have become a problem when he immigrated to the U.S., for the State Department manual says that Vitezi Rend members “are presumed to be inadmissible.” Karl Pfeifer, an Austrian journalist who has long specialized in Hungarian affairs, told me that Gorka unquestionably had worked with racists and anti-Semites in Hungary.

Gorka and the White House did not respond to my inquiries. But Gorka told The Tablet website that he had never been a member of Vitezi Rend and used the v initial only to honor his father. He has robust defenders, who say he has never shown a hint of racism or anti-Semitism.

As Ana Navarro, a G.O.P. strategist, tweeted: “Donald Trump attracts some of the shadiest, darkest, weirdest people around him.”

In fairness, Trump has also appointed plenty of solid people: Jim Mattis, Elaine Chao, H. R. McMaster, Dina Powell, Gary Cohn, Steven Mnuchin and more. And Trump’s Supreme Court nominee, Neil Gorsuch, is a first-rate lawyer.

Yet Trump’s record of appointments over all suggests a lack of interest in expertise. I’m not sure that this is “the worst cabinet in American history,” as a Washington Post opinion writer put it, but it might be a contender. The last two energy secretaries were renowned scientists, one with a Nobel prize, while Trump appointed Rick Perry — who once couldn’t remember the department’s name.

Trump appointed his bankruptcy lawyer, David Friedman, to be ambassador to Israel. He chose Jason Greenblatt, another of his lawyers, to negotiate Mideast peace. He picked Omarosa Manigault, who starred with him on “The Apprentice” and has a record of inflating her résumé, to be assistant to the president.

The director of Oval Office operations is Keith Schiller, a former Trump bodyguard best known for whacking a protester. And the Trump team installed as a minder in the Labor Department a former campaign worker who graduated from high school in 2015, according to ProPublica.

So see the failure of the Republican health care bill through a larger prism: The measure collapsed not just because it was a dreadful bill (a tax cut for the wealthy financed by dropping health coverage for the needy). It also failed as a prime example of the Trump administration’s competence gap.

Democrats may feel reassured, because ineptitude may impede some of Trump’s worst initiatives. But even if Trump is unable to build, he may be able to destroy: I fear that his health care “plan” now is to suffocate Obamacare by failing to enforce the insurance mandate, and then claim that its spasms are inevitable.

Of all the national politicians I’ve met over the decades, Trump may be the one least interested in government or policy; he’s absorbed simply with himself. And what we’re seeing more clearly now is that he has crafted an administration in his own image: vain, narcissistic and dangerous.

<NICHOLAS D. KRISTOF>