When the last American soldier flew out of Afghanistan on Aug. 30, 2021, leaving the country to Taliban rule, the world braced for a human rights nightmare.

In that sense, the Taliban have met expectations. The country’s extremist rulers, who seized power from an American-backed government of 20 years, have carried out revenge killings, torture and abductions, according to international observers. They have also imposed the world’s most radical gender policies, denying education and employment to millions of Afghan women and girls — even shutting down beauty parlors.

On Aug. 14, a group of United Nations officials issued a report saying the Taliban had engaged in “a continuous, systematic and shocking rescinding of a multitude of human rights, including the rights to education, work, and freedoms of expression, assembly and association.”

Some analysts and U.S. officials had clung to the hope that the Taliban had moderated since they last controlled the country in the 1990s, or that they would at least make concessions to Western demands on human rights to win diplomatic recognition or economic aid as the country suffers a deepening humanitarian crisis.

It was not to be.

“The concept of a ‘reformed’ Taliban has been exposed as mistaken,” the U.N. experts wrote.

As a result, Biden administration officials have ruled out the possibility that they would agree to Taliban demands for international recognition, sanctions relief and access to billions of dollars of assets frozen in the United States.

At the same time, aspects of Taliban rule have modestly surprised some U.S. officials. Fears of civil war have not materialized, and the Taliban have cracked down on corruption and banned opium poppy cultivation, although it remains to be seen how strictly the ban will be enforced.

And on President Biden’s top priority for the country — preventing a return of terrorist groups that might threaten the United States — the Taliban leaders appear to be meeting Washington’s approval. That is crucial, given that the United States invaded Afghanistan in 2001 because the Taliban harbored leaders of Al Qaeda who plotted the Sept. 11, 2001, attacks.

“I said Al Qaeda would not be there,” Mr. Biden said on June 30, in response to a reporter’s question about the American withdrawal. “I said we’d get help from the Taliban. What’s happening now?”

The question was rhetorical; Mr. Biden’s clear implication was that he had been vindicated by his decision to withdraw American troops.

That has not been enough to persuade Mr. Biden to restore any U.S. support to the country. But some humanitarian groups and Afghanistan experts are calling on the Biden administration to soften its position and, at a minimum, provide the Taliban with direct economic assistance to alleviate the country’s desperate poverty and hunger.

“The world needs to think hard about what it’s trying to achieve in Afghanistan these days, and most of the stuff we want to do requires working with the Taliban,” said Graeme Smith, an analyst at the Crisis Group who has worked in Afghanistan since 2005 and recently spent months in the country assessing conditions under Taliban rule.

Mr. Smith recently wrote an essay in the publication Foreign Affairs urging Western governments and institutions “to establish more functional relationships with the Taliban.” That could include assistance with the country’s electricity grid, banking system and water management, Mr. Smith said.

The need is especially acute, Mr. Smith added, given that international humanitarian aid — which the United States and other countries currently send directly to aid groups, circumventing the Taliban government — has been dwindling.

Such cooperation is unlikely in the near term, Mr. Smith said, given what he called the “toxic politics” of Afghanistan. Republicans have attacked Mr. Biden for what they called a poorly managed and undignified exit from the country, a dynamic that may be making the president more risk averse.

“If Biden is re-elected, that will buy him a little bit of operating space for some practical solutions,” Mr. Smith said.

Taliban officials say U.S. policies are exacerbating suffering in Afghanistan, because longstanding American sanctions against Taliban leaders discourage foreign investment and trade in the country.

They insist that the United States has no right to hold $7 billion in assets deposited by their predecessors at the Federal Reserve in New York. (Mr. Biden last year ordered half that money into a trust for the humanitarian needs of Afghanistan’s people.)

The Biden administration has some contacts with Taliban representatives. Over the past two years, Thomas West, the State Department’s special representative for Afghanistan, has traveled to Doha, Qatar, for several meetings with Taliban officials, most recently on July 30 and 31.

An official State Department description of that session criticized the Taliban and “the deteriorating human rights situation in Afghanistan, particularly for women, girls and vulnerable communities,” and said U.S. officials “expressed grave concern regarding detentions, media crackdowns and limits on religious practice.”

But the summary also offered some positive words about declining opium poppy production, promising economic indicators and counterterrorism efforts, and it hinted that further cooperation might be possible. At a meeting with Afghan government finance and banking officials, the description said, Mr. West and his colleagues “voiced openness to a technical dialogue regarding economic stabilization issues soon.”

On Wednesday, the White House released a statement from Mr. Biden marking the second anniversary of the war’s end. “We have demonstrated that we do not need a permanent troop presence on the ground in harm’s way to take action against terrorists and those who wish to do us harm,” Mr. Biden said. He added that the U.S. is the world’s largest donor of humanitarian assistance for the country.

When it comes to cooperation against terrorism, however, some officials and analysts remain deeply mistrustful, fearing that the Taliban are merely containing Al Qaeda in the short term to avoid provoking the United States. The Taliban are also battling a local branch of the Islamic State terrorist group. But some say that means little, given that the Islamic State openly challenges Taliban rule, making such operations clearly in the Taliban’s self-interest.

“Seeking to engage the Taliban on terrorism while ignoring what they do to women is a mistake,” Lisa Curtis, a National Security Council official in the Trump White House, said at a panel hosted by the Middle East Institute in July.

The Biden administration draws clear limits on such contacts, however. “Any kind of recognition of the Taliban is completely off the table,” a deputy State Department spokesman, Vedant Patel, told reporters in April. And officials say American diplomats will not return to Kabul, the capital, any time soon.

Zalmay Khalilzad, who served as President Donald J. Trump’s envoy to the Taliban and negotiated the troop withdrawal plan that Mr. Biden inherited, argued for a change in U.S. policy. “We have wished the problem to go away,” he said.

Mr. Khalilzad is among those who say that, relative to the worst expectations, the Taliban have shown some restraint.

“Many thought things would be a lot worse than they are — that there would be a lot more terrorism, a lot more refugees, and that there would be bloodshed” on a much wider scale, he said.

But granting the Taliban any credit remains highly controversial. Last month, a senior Conservative Party member of Britain’s parliament, Tobias Ellwood, traveled to Afghanistan and posted a video declaring it “a country transformed” — in many ways for the better. “Security has vastly improved, corruption is down, and the opium trade has all but disappeared,” he asserted, adding that the economy was growing.

Mr. Ellwood called for Britain to reopen its embassy in Kabul, which was shuttered in August 2021, and for his government to engage with the Taliban rather than “shout from afar.”