In a high-profile arrest in 2014, a man dressed as Spider-Man punched an officer in the face. Other characters have been caught in other scuffles or accused of using explicit language.

Times Square has been a victim of its own success, said Councilman Corey Johnson, a sponsor of the bill. Performers should be able to make an “honest buck” in the plazas, he said, but some go too far. “People should be able to walk through Times Square without being harassed and harangued,” said Mr. Johnson, a Democrat.

After the issue erupted last summer, Mayor Bill de Blasio said he would consider removing the plazas, prompting criticism from transportation groups that said the plazas had improved traffic safety. Police Commissioner William J. Bratton said he wanted to “dig the whole damn thing up.” Gov. Andrew M. Cuomo was not far behind, saying the topless women undermined the family-friendly nature of the square the city wanted to promote.

On Thursday, several performers in superhero costumes came to the Council Chambers to defend their profession. Abdel Amine Elkhezzani, a Spider-Man performer in Times Square, said he would lose most of his business if he had to stay in a certain zone.