Some former allies grew disillusioned. Mr. de Blasio waited until late in his second term to phase out the gifted and talented program for elementary schools, and to open supervised drug injection sites. A plan to create 100,000 jobs that paid $50,000 or more faced criticism for not doing enough to include New Yorkers in the city’s poorest neighborhoods.Bertha Lewis, president of the Black Institute, who helped Mr. de Blasio win over progressives during the 2013 Democratic primary for mayor, said it became difficult to defend Mr. de Blasio because he failed to act on key issues. His allies wanted the all-hands on deck approach that the mayor had used to win prekindergarten to confront other issues like public housing but Mr. de Blasio often seemed unwilling to risk the political capital to do so.Ms. Lewis called universal prekindergarten “an incredible accomplishment,” but said that the program alone was not enough to declare victory against inequality.“How long are you going to ride that surfboard?” she said.James Parrott, an economist with the Center for New York City Affairs at the New School, said Mr. de Blasio does not get enough credit for “actively using policy to actually reduce poverty,” including instituting other labor protections like settling union contracts.Workers in the bottom half of the economy saw a 15 percent increase in wage share from 2013 to 2019, while the rest of the country held steady, according to Mr. Parrott’s analysis of data from the Independent Budget Office.The discount MetroCard proposal seemed to fit squarely within Mr. de Blasio’s left-wing rhetoric. Mr. Jones pitched the idea to the mayor, and Mr. de Blasio liked it so much that he called Mr. Jones and said he was going to appoint him to the board of the Metropolitan Transportation Authority to help see it through.“Almost immediately after that, he began moon-walking away from it,” Mr. Jones said.Mr. de Blasio unsuccessfully argued that Mr. Cuomo should pay for the program since he ran the subway. At the same time, the mayor announced significant city funding for a heavily subsidized ferry system that is used mostly by affluent, white New Yorkers.