Yet the Trump connection may actually be more of a liability, people close to the firm contend.
That's because of differences over both style and substance, as well as the constant scrutiny a company naturally falls under when five of its former executives are named to prominent government positions.
Other big financial institutions, including the money manager Fidelity and the private equity firm Warburg Pincus, can claim only one former executive apiece among those put forward for major staff or secretary roles in the Trump administration.
Despite its numbers in Washington, Goldman's chief executive, Lloyd C. Blankfein, is taking issue with the perception of coziness between his company and the White House.
"We have been criticized for the fact that some of our colleagues, after long careers at the firm, have moved to work in the public sector," he wrote on Thursday in a letter to investors. "The charge is that Goldman Sachs is able to extract certain advantages that others cannot. In fact, the opposite is true. Those in government bend over backward to avoid any perception of favoritism."
Still, two days before his letter surfaced, Mr. Blankfein was reportedly spotted at a Four Seasons hotel bar in Washington having drinks with Gary D. Cohn and Dina Powell. Mr. Cohn resigned as Goldman's president in December to become the director of the National Economic Council, and Ms. Powell ran Goldman's philanthropic investing before being named a presidential adviser and, this week, deputy national security adviser for strategy.
Mr. Cohn has recused himself from Goldman matters on the job, the White House has said. Goldman officials who are close to Mr. Cohn and other former colleagues now in government have said they are restricting their communications largely to social conversations.
If there is a mind meld between Goldman and the Trump administration, it has been fractured at times.
Some of the White House's early policies, including the Jan. 27 travel and immigration ban and moves to roll back lesbian, gay, bisexual and transgender rights, have sat poorly with senior Goldman executives, whose thinking on social issues has proved to be more liberal than Mr. Trump's.
Conversations between Goldman employees and their former colleagues in Washington, meanwhile, have come under scrutiny. Two Democratic senators recently demanded records of any communications between Goldman and its alumni in the Trump administration that involved discussions of certain economic policies. Goldman's lawyer denied involvement by the firm.
And being intimately linked to a president whose incoming approval ratings were at a historic low may not burnish the firm's image as ties to past administrations did.
"My guess is that whatever benefit Goldman would have from its senior executives leaving to go to the Trump administration, the reputational effects may well be more severe," said Peter Conti-Brown, a financial historian who teaches at the Wharton School.
Among other things, he added, Mr. Trump's more polarizing policies on issues that a younger generation of workers hold dear could create recruitment problems for the bank. For instance, Mr. Conti-Brown said, most of the business school students he encounters at Wharton espouse a more globalist view than the "America First" brand of economic nationalism championed by Mr. Trump and his chief strategist, the onetime Goldman investment banker Stephen K. Bannon. And they expect to work in places that value diversity of gender and sexual orientation.
"If the best and brightest look at Goldman Sachs as an appendage of the Trump administration and react with horror," Mr. Conti-Brown said, "they'll be looking more closely at jobs with Morgan Stanley" — one of Goldman's closest competitors on Wall Street.
The ties between Goldman Sachs and the Trump administration are extensive. In addition to Mr. Cohn, Mr. Bannon and Ms. Powell, the new Treasury secretary, Steven Mnuchin, served on Goldman's management committee. And James Donovan, who has been named Mr. Mnuchin's deputy, was a longtime wealth-management and banking executive at Goldman.
There are less-obvious examples as well: the Goldman board secretary who worked on the secretary of state's transition, and the private-practice lawyer who counts Goldman as a major client and was nominated to be chairman of the Securities and Exchange Commission.
Goldman's generous pay and burnout-inducing hours have created an environment where retiring in one's late 40s or early 50s is not unusual. At that stage, with their health still intact and their earnings not an object, Goldman alumni often seek out a second, more mission-oriented career.
"I'm going on to a spectacularly new challenge," Mr. Cohn said in an interview as he prepared to leave the firm. He has since added that he's excited about helping create jobs and expand the economy.
Henry M. Paulson Jr., the onetime Goldman chief executive who became Treasury secretary in 2006, did it partly for posterity. Ready to turn the post down, he was swayed, according to several accounts, when a friend said: "You don't want to be sitting around at 80 years old telling your grandchildren you were once asked to be secretary of the Treasury. You should tell them you did it."
Serving in high-ranking government positions has been a long tradition among Goldman's departed executives, who are prominent in both parties. Nonetheless, that could change after the Trump administration.
The first attempt by the president to block travelers from predominantly Muslim countries, in January, illustrated how the White House and Goldman could be at odds.
Two days after the order was issued, Mr. Blankfein — who was concerned about the impact on employees and their families as well as about recruiting efforts — leveled a very public objection.
"This is not a policy we support," he said in a voice mail message that was dispatched to 34,000 company employees, "and I would note that it has already been challenged in federal court."
Around that time, a draft of an executive order to roll back lesbian, gay, bisexual and transgender workplace protections, put in place during the Obama administration, was circulating around the White House. The plan clashed head-on with the more liberal workplace policies on Wall Street, especially at Goldman, where Marty Chavez, the incoming chief financial officer, is gay.
Ultimately, the White House order was shelved, thanks in part to criticisms from Mr. Cohn. But Mr. Trump's separate decision, made in late February, to rescind the rights of transgender students to use bathrooms of their preference was issued.
The details of policies that stand to benefit Goldman, including the defanging of the Dodd-Frank Act, corporate-tax cuts and a promised $1 trillion in infrastructure spending, have yet to emerge.
Even so, Goldman's critics on the left, including Senator Elizabeth Warren, the Massachusetts Democrat who has said Mr. Cohn's role as the president's most senior economic adviser "turns my stomach," seem emboldened.
For Mr. Blankfein and other Goldman executives who worked closely with Mr. Cohn and Ms. Powell, the limits on contact may be the most awkward new development.
When Goldman employees run into their former colleagues now working at the White House, "everyone just needs to learn to talk weather and sports," said a Goldman spokesman, Jake Siewert, who left a job at the aluminum company Alcoa for a Treasury post in 2009 and faced similar issues.
"For better or worse" at Goldman Sachs, he added, "we have learned to run our business under intense public scrutiny."
The spotlight on Mr. Trump's favored bank is unlikely to grow dim any time soon.
The Royal Bank of Scotland chairman's quip, delivered on Feb. 24, was one clue.
"It was just a joke," Mr. Davies said in an interview. The Royal Bank of Scotland was reporting a 7 billion pound loss that day, "which was not exactly anything to celebrate in a conventional way."
Still, "if you look around, the head of the Bank of England was at Goldman, the head of the E.C.B. was at Goldman," Mr. Davies added, referring to the European Central Bank. "This is not just an American phenomenon. Goldman alumni are everywhere."