POLITICAL REALITY has a way of undoing populist campaign promises. But to the delight of many a Democratic activist, New York’s new mayor, Bill de Blasio, roared into office on New Year’s Day, declaring that this time will be different.

In his inaugural address, Mr. de Blasio, an unabashed “progressive” who ran on a pledge to end the Big Apple’s glaring income inequality, did not trim his vows to raise income taxes on high-earners, expand preschool, require mandatory sick leave and require developers to build affordable housing. His goal, he said, is “that New Yorkers see our city not as the exclusive domain of the 1 percent but a place where everyday people can afford to live, work and raise a family.”

To the Democratic left, Mr. de Blasio looks like an authentic liberal antidote to the Obama administration’s compromises — and a harbinger of progressive revival nationwide.

Inequality is a glaring issue for New York, which is why Mr. de Blasio’s theme — “a tale of two cities” — caught on. With thousands of Wall Street moguls and millions of striving immigrants, New York has the least equal income distribution of any U.S. city with more than 500,000 residents except Atlanta and the District, according to a 2011 Census Bureau study. Mr. de Blasio is right to focus attention, and policy, on the imbalance.

Of course, inequality is a national phenomenon, not easy to dent one city at a time. Mr. de Blasio can’t even raise income taxes on those making $500,000 or more, as promised, without the approval of New York Gov. Andrew M. Cuomo (D) and the state legislature. Otherwise he’ll have to come up with the half-billion dollars he plans to spend on preschool somewhere else.

Our bigger concern is that Mr. de Blasio might undermine efforts that would generate more equal opportunity in the long run. Achieving this goal is not just a matter of taxing and spending but also of institutional reform — especially in education. His predecessor, Michael R. Bloomberg (I), challenged teachers unions and other entrenched interests to expand school choice and accountability. He closed large neighborhood schools that were performing poorly and replaced them with hundreds of smaller schools and public charter schools. When Mr. Bloomberg became mayor in 2001, fewer than half of New York City’s high school students graduated in four years; that figure is now 61 percent, even though standards are tougher. Fourth-grade reading and math scores have risen, albeit slightly.

School reform in New York is still a work in progress, but Mr. de Blasio seems to side with those who want to scrap Mr. Bloomberg’s efforts rather than build on them. He has promised to limit charter schools’ access to publicly owned buildings, impose a moratorium on closing low-performing schools and end Mr. Bloomberg’s A-to-F report cards for schools. His choice for schools chancellor, Carmen Fariña, is a prominent critic of Mr. Bloomberg’s approach who quit the former mayor’s administration over “philosophical differences.”

Of all the ways to reduce inequality, none is more important than giving poor children access to good schools — including, but not limited to, pre-K. And of all the political forces that propelled Mr. de Blasio into office, none is less truly progressive than the backlash against school reform.