"Cigar Man" and several other homeless people in the District take shelter at a Metro stop in January. (Amanda Voisard/For the Washington Post)

Driving into the nation’s capital along New York Avenue reveals an American social smash-cut.

About three miles from the U.S. Capitol, women with umbrella strollers, heavy bags and a hand-chain of children in tow are dodging traffic to cross the busy Northeast Washington thoroughfare. Especially early in the morning, they walk in waves, with school-uniform skirts and baby fleece blankets flapping in the back wind of the traffic roaring by.

They’re not tourists leaving low-budget motels for a day of sightseeing. Nor are they hipster newcomers heading to the shiny, new craft distillery and tasting bar, the Nike store, the organic market or the Bikram hot-yoga studio, all of which have popped up along New York Avenue.

They’re homeless, and their families are living in motel rooms paid for by the District. We created this desperate situation.

Last year, Washington ranked as having the highest rate of homelessness among U.S. cities, according to a survey by the U.S. Conference of Mayors, and, in 2015, as being the most expensive city in the United States to raise a family, according to the Economic Policy Institute.

Here’s the news that makes this affordability and homelessness crisis really heartbreaking: Besides having the highest percentage of homeless people, the District also forfeited millions of dollars in federal money that could have helped them live in real homes. No other housing agency in the country has returned more ­affordable-housing money — nearly $16 million — to the U.S. Department of Housing and Urban Development than the District, my Post colleague Debbie Cenziper reported over the weekend.

And that is shameful.

Or as Will Merrifield, a lawyer at the nonprofit Washington Legal Clinic for the Homeless, put it: “This is insane. That they would allow this money to go to waste is absurd.”

The HUD funding provides seed money to developers willing to create low-income housing, provides down-payment assistance to buyers, and funds vouchers for families as part of the HOME Investment Partnerships Program.

The incompetence that allowed millions of dollars to be forfeited cannot be tolerated any longer. There is a moral imperative to create permanent affordable housing before the District morphs into Manhattan.

The legal clinic issued a report last week showing that besides losing all that federal money, the city’s keystone program for ending family homelessness — rapid rehousing — is hardly a success.

“We’ve raised concerns about the [rapid rehousing] program since its inception,” said Patricia Fugure, executive director of the legal clinic. “In a jurisdiction with housing as expensive as in D.C., the math simply doesn’t work.”

District leaders claim the program, which places homeless families in apartments with subsidies that are eventually removed, is 85 percent successful.

But the legal clinic’s report, “Set Up to Fail,” couldn’t be more aptly named. In the past few years, nearly every homeless parent I meet at the city’s decrepit shelter at the former D.C. General Hospital says they were one of the 4,000 families that have cycled through the rapid rehousing program.

Not only do District families find themselves unable to afford the apartment they were placed into — remember, the median cost for a one-bedroom apartment in the District is $2,000 a month — another eviction and a move back into a homeless shelter retraumatizes the family, disrupting school routines, friendships, sports schedules and work commutes.

The key suspect in all of this is failed bureaucracy, for sure.

Mayor Muriel E. Bowser’s administration is looking at a department it found in disarray and unable to meet the complex demands of federal housing funds. It’s not just a check they got in the mail and forgot to cash. Federal money is tied to meeting certain goals, deadlines, requirements and specifications.

“We knew that we inherited something that wasn’t functional in the way that it needed to be, and the team has been very good at turning that ship around,” Andrew Trueblood, chief of staff to the deputy mayor for planning and economic development, told The Post.

But it takes more than a streamlined bureaucracy to fix an affordability crisis that keeps getting worse.

A city needs people of all income levels to function, but it cannot function unless people of all income levels can afford to live here.

Washington was not the homeless capital of the nation before it became a hot place to live — see the connection?

Affordable housing requires real, permanent solutions, not smoke and mirrors. And no dollars — or pennies — that can help solve the problem should ever be left on the table.

Twitter: @petulad