As the dream of banning cars becomes a reality Wednesday on San Francisco’s Market Street — an idea dating to when horse-drawn buggies jockeyed for space among puttering Ford Model Ts — one top transportation official is already pitching ideas for the next car-free thoroughfare.

During a San Francisco Municipal Transportation Agency board meeting Tuesday, Chair Malcolm Heinicke called for automobiles to be purged from Valencia Street, a bustling strip in the Mission District.

“I’m not very patient here. I want the next one,” Heinicke told The Chronicle outside the meeting where he and the other six directors discussed themes for the coming year.

He predicts that Market Street sans cars will reap huge benefits for pedestrians, cyclists and buses. Analyses by SFMTA suggest that Muni’s buses and streetcars will run 15% to 25% faster. Planners also expect to substantially reduce collisions, providing a safe path for the 500,000 people who walk along Market Street daily.

Residents and visitors could enjoy similar advantages on Valencia if cars no longer ruled the road, Heinicke said.

His pitch had activists cheering on social media. But the vice president of the Valencia Corridor Merchants Association was stunned.

“I personally think it would be devastating to our business,” said Jonah Buffa, co-owner of Fellow Barber at 18th and Valencia streets. Many of his customers arrive by car, whether driving their own vehicles or riding an Uber or Lyft.

The strip has long been contested ground, where cyclists, scooter riders and pedestrians weave between ride-hail vehicles and delivery trucks. Bike advocates who pressed for protected bike lanes found a champion in Mayor London Breed, who two years ago directed the SFMTA to place barriers along a four-block segment between Market and 15th streets.

Since then, improvements have been “insanely” slow, said cyclist Matt Brezina. He and other activists routinely pack City Hall hearings and rally on social media, pressuring the city to build more car-free infrastructure. On Sunday, Brezina helped lead a protest ride along John F. Kennedy Drive in Golden Gate Park to call for the removal of cars on that roadway as well. State Sen. Scott Wiener and Assemblyman David Chiu, both San Francisco Democrats, attended.

Heinicke said he is open to banning cars on JFK Drive, though it’s slightly more complicated because the city’s Recreation and Park Department would have to approve. Now, however, Valencia is his chief target.

“When you look at the maps and the presentations ... one street cries out to me,” he said. “And that’s Valencia Street.”

Though city officials widely embrace the “Better Market Street” car ban, calling it an expression of their leadership on traffic safety, environmentalism and urban design, the idea took years to gain momentum. Last year Heinicke asked the SFMTA to develop proposals for other car-free streets, but the plans have yet to materialize. He’s frustrated with the lack of progress.

“As I’ve learned from pushing this Market Street thing for all of these years, if you don’t get started now, it won’t get finished,” he said.

Tom Maguire, director of the agency’s Sustainable Streets division, said he’s taking Heinicke’s comments seriously, and said his division would come up with a list of potential car-free streets in two months. But he cautioned that the agency’s first priority is extending the protected Valencia Street bike lane.

City transportation chief Jeffrey Tumlin said changes to Valencia could come in a more nuanced form than an outright vehicle ban, such as removing cars at certain times or days.

“And we don’t think about the whole mile and a half of Valencia,” Tumlin said. “We can think about it block by block.”

He cautioned that any dramatic change to the street should have support from the community, rather than being a top-down directive from City Hall. Successive waves of gentrification have rattled the Mission District for decades, and many longtime residents see any reconfiguration of the roadway as part of the problem, saying it could drive up property values.

Heinicke, by contrast, is losing patience with the endless political compromises that can waylay a big transportation project. He had pushed for nearly a decade to banish cars from Market Street, and now he wants to see that replicated on boulevards throughout the city.

“We need to look at another street to make a complete transit, bike and pedestrian priority,” he said. “And I’m not talking about two blocks. We’re thinking big here.”

Rachel Swan is a San Francisco Chronicle staff writer. Email: rswan@sfchronicle.com Twitter: @rachelswan