Sen. Elizabeth Warren's request that the Federal Reserve continue to limit growth at Wells Fargo as long as Chief Executive Officer Tim Sloan is running the company is unlikely to force him out, one analyst says, but the tarnished lender is paying a steep political price for its loyalty.

Warren has long argued that Sloan, who held senior leadership roles during a series of scandals including the creation of 3.5 million unauthorized accounts, should be fired, a suggestion he has dismissed. On Thursday, the Massachusetts Democrat raised the stakes with a letter to Fed Chairman Jerome Powell arguing that Wells Fargo can't meet the Fed's conditions for lifting the growth cap with Sloan at the helm.

The Fed's early February order barred the San Francisco-based lender from expanding its total assets beyond the nearly $2 trillion it held at the end of 2017 until it sufficiently improves its oversight and risk management.

While "there is little that Sen. Warren can do to force the Federal Reserve to remove Sloan," said Jaret Seiberg, an analyst with Cowen Washington Research Group, that doesn't mean that Wells Fargo should keep him.

"The politics here are terrible no matter what the bank does," Seiberg added. While Sloan wasn't promoted to CEO until his predecessor, John Stumpf, resigned after fiery congressional hearings over the fake accounts in late 2016, he had previously served as chief operating officer and chief financial officer.

Since he "was in senior management when the trouble occurred," Seiberg said, "he always will be associated with the fake accounts and other controversies. As long as he remains, Democrats will be on the attack."

Unless Democrats regain majorities in the Senate as well as the House, however, Warren may be "close to exhausting her ability to exert political pressure on the Federal Reserve to maintain the asset cap," Seiberg added. He predicts the limits will remain in place until late 2019, unless further regulatory problems are uncovered at the bank, something Sloan told investors last week he hopes to avoid.

Wells Fargo said Thursday it "continues to have constructive dialogue with the Federal Reserve" regarding the operational and oversight concerns detailed in the central bank's consent order that established the growth restrictions.

"We are also confident that the transformation of the company over the last two years, including our efforts to make things right with our customers, will contribute to resolution of the issues cited within the consent order, especially in our operational and compliance risk-management structure,” Wells Fargo said in a statement that didn't directly address Warren's letter.

The bank has grappled with further problems since the order was imposed, however. In April, it agreed to pay $1 billion in civil penalties to settle investigations of its automotive- and mortgage-lending practices. The government said the lender had sold some auto borrowers insurance they didn't need under the pretense they might not qualify for the loans otherwise, and charged fees to mortgage customers that it was supposed to be absorbing.

Then, in August, Wells Fargo agreed to pay $2.09 billion to settle Justice Department allegations that the bank packaged mortgages that were higher-risk than they appeared into securities sold before the 2008 financial crisis. Bank officials were aware that the borrowers had misstated their incomes, the department said, which would impede their ability to repay the loans.

Such securities, which had been awarded the highest credit ratings and were widely held by investors including large Wall Street firms, became impossible to value after a housing bubble began to collapse in 2006 and home owners defaulted on their debt.

Cascading losses in the $15 trillion mortgage market, the largest in the U.S., ultimately spurred the collapse of investment bank Lehman Brothers and forced the government to spend billions on bailouts to shore up the financial system.

"Wells Fargo is fundamentally broken," Warren argued in her letter to the Fed's Powell. "Over the last decade, it has regularly engaged in illegal or otherwise improper conduct that has hurt millions of its customers and employees."

As a result, "the Federal Reserve should not remove the growth cap on Wells Fargo until the board replaces Mr. Sloan with a new CEO who has not contributed to the very problems the Federal Reserve is seeking to fix," she said.

Wells Fargo fell 2.5 percent to $53.10 on Thursday amid a broader selloff in U.S. stocks.