The breathless coverage of a Trump White House reportedly gripped by palace intrigue is enough to keep a reader’s head spinning.

Chief strategist Steve Bannon is about to be fired. Or will he quit? Maybe neither, but his clout has certainly waned. Stephen Miller, once a Bannon acolyte, is now aligned with Trump son-in-law Jared Kushner. Economic adviser Gary Cohn, a Wall Street man and past donor to top Democrats, also now has President Trump’s ear.

All of this may sound like so much schoolyard gossip, but it matters. The declining White House status of the populist-nationalist Mr. Bannon has telegraphed the rise of the more-moderate, establishment-oriented “globalists” – foremost, Mr. Cohn, Mr. Kushner, and his wife, Ivanka Trump.

That, in turn, has led to a stark turnabout by Trump on a range of issues: NATO is no longer derided as “obsolete.” China will not be branded a “currency manipulator.” Trump no longer wants to eliminate the Export-Import Bank. He might reappoint Janet Yellen as Federal Reserve chair. And last week, Trump ordered air strikes against the Syrian government, after years of tweeting that the US should not intervene.

All of this points to a core fact about Trump that was well-known from the beginning of his campaign – that above all, he is results-oriented.

“What could make the Trump presidency successful is that he’s not wedded to a particular ideology,” says Republican strategist Ford O’Connell. “Donald Trump was not elected to be president of the Republican Party or a doctrinaire conservative. He is about putting people back to work and getting things done, and he’ll move around the spectrum to do it.”

Some campaign promises remain sacrosanct. A conservative, Neil Gorsuch, has filled the long-vacant Supreme Court seat. The Trump administration is cracking down on illegal immigration, and putting together a national deportation force. Plans for a wall on the US-Mexico border continue apace.

Trump is also proceeding with plans to reduce the size of government and eliminate regulations. Though he lifted his federal hiring freeze this week, he has tasked his budget office with crafting a plan to cut the federal workforce. That’s in keeping with Bannon’s goal of “deconstructing the administrative state.”

Smaller role for Bannon

But Bannon himself is, by many indications, being marginalized. Last week Trump signed off on Bannon’s removal from the principals’ committee of the National Security Council, a move orchestrated by the new national security adviser, H.R. McMaster. Trump also ordered Bannon and chief of staff Reince Priebus to work out their differences with Kushner.

This week, Trump belittled Bannon in two newspaper interviews. “Trump won’t definitively say he still backs Bannon,” read The New York Post headline. In the story, Trump said that he liked Bannon, but noted that he had joined the campaign late, after winning the GOP nomination. “I’m my own strategist,” Trump said, a line he repeated the next day to The Wall Street Journal.

Bannon’s problem isn’t necessarily his ideology. By the president’s own accounting, Trump likes to hear competing points of view and then make his decisions. The problem is that Bannon quickly attained a larger-than-life profile – dubbed “President Bannon” (mostly by Trump foes), appearing on the cover of Time magazine as “The Great Manipulator,” depicted on “Saturday Night Live” as the Grim Reaper.

Trump does not like to be overshadowed. His modus operandi is “never stop being the center of attention,” says Trump biographer Gwenda Blair.

Another non-negotiable with Trump is his family. “Bannon got himself caught up in family business, and it’s unwinnable for him,” says Mr. O’Connell. “The question is not, is his influence diminished, but can he stay in the administration.”

There is some suggestion that it might be safer for Trump to keep Bannon inside the tent than to kick him out. But the larger question may be: How did Bannon go from being a critical member of Trump’s inner circle to being elbowed out?

“I think Steve made an error by not spending any of his political capital to bring other Trump-ites and non-globalists into the White House circle,” said Roger Stone on “Meet the Press Daily” Thursday. “Therefore now he’s alone and he’s surrounded.”

Mr. Stone, a longtime Republican operative and informal Trump adviser, added that he thinks his friend Bannon, perhaps unfairly, “takes the rap for the fiasco surrounding health care” – a reference to the failed effort in the House to repeal and replace the Affordable Care Act. Stone said he felt Mr. Priebus “should be wearing a bit more of that.”

“The travel ban is also probably counting against him,” Stone said, referring to the administration’s efforts to temporarily ban non-US travelers from certain countries from entering the country – an initiative that is on hold in the courts. “Though I would argue that in Donald Trump’s case he only suffers politically not when he’s defeated but when he stops trying.”

Shakeup inevitable?

All administrations go through growing pains. President Bill Clinton’s loose style led to early shakeups of his White House. President Jimmy Carter also struggled, surrounding himself with people from his home state of Georgia and not enough experienced Washington hands. Trump, like other “outsider” presidents, has eschewed insiders, but as a result, he has an inner circle that lacks governing experience.

Just four months into his presidency, Mr. Clinton, a Democrat, brought in David Gergen, who had advised three previous presidents, all Republicans. As Trump closes in on the symbolically important 100-day mark in office, Washington observers are waiting for the inevitable shakeup, and watching to see if Trump brings in any “wise men” – or women.

Increasingly, Trump is bringing people like him, wealthy New Yorkers, into his inner circle – people like Stephen Schwarzman, CEO of Blackstone Group, now an informal counselor to the president. It’s a natural human impulse to surround oneself with people who have a similar background and worldview. Goldman Sachs has a large contingent of alumni in Trump world, including Cohn, Treasury Secretary Steve Mnuchin, and Deputy National Security Adviser Dina Powell.

Bannon is also a Goldman alum, but stylistically and ideologically he is not of that world. His scruffy appearance and adherence to a controversial theory about cycles of history set him apart. Before joining the Trump team, Bannon was CEO of Breitbart News, which was known for nationalist-populist content that is at times racist and misogynist.

Now, it seems, the Bannon phase of Trump’s presidency is fading, and a more moderate, pragmatic approach is ascendant – at least in some areas. Trump is eager to cut a deal with Democrats on health-care reform, as a prelude to what he sees as his most important initiative, tax reform.

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Whether Trump can pull off either initiative is questionable, given the highly partisan atmosphere on Capitol Hill. For Trump supporters, the jury is still out. Polls show most Trump voters are sticking with him so far. And all the internal drama at 1600 Pennsylvania Avenue matters less than whether Trump can fulfill his most important promises: to make their lives better and give Americans a better sense of security.

“The daily up and down won’t matter as much as, does the economy continue to improve, do they actually come up with some solutions on health care, are they able to resolve Syria and North Korea,” says Thomas Schwartz, a political historian at Vanderbilt University in Nashville, Tenn. “Those things will be much more important by the time you get to the midterms and the 2020 election.”