New York Gov. Andrew Cuomo (D) and Sen. Bernie Sanders (I-Vt.). (Mary Altaffer/Associated Press)

NEW YORK Gov. Andrew M. Cuomo (D) announced last week a plan to provide free in-state tuition to many New Yorkers. In the process, he got his picture taken with Sen. Bernie Sanders (I-Vt.) and burnished his image with progressives, whose support would help him in a presidential run in 2020. Just one problem: His plan is not particularly progressive. In fact, as Urban Institute education expert Matthew M. Chingos explained on The Post’s higher-education blog, its benefits would largely flow to middle- and upper-middle-class families, not to the neediest.

Mr. Cuomo proposed spending $163 million to eliminate tuition payments for students who are enrolled full time in public undergraduate degree programs and whose families make $125,000 or less. The aid would come in the form of new Excelsior Scholarships, which would pay the difference between the grant aid that students currently get and the cost of tuition at state colleges, which runs about $6,000 to $7,000 per year.

Students from low-income families already get aid packages from the federal and state governments that cover tuition costs, so the benefit would not go to them — even though they still need help. In fact, very needy New York families require more help financing non-tuition costs such as room, board and books than middle-class families need with New York’s modest tuition charges. But Mr. Cuomo’s plan would pump more aid to families that make more money. The more tuition students are currently expected to contribute — that is, the higher their families’ incomes — the larger the benefit they would receive under Mr. Cuomo’s scheme.

It is true that college costs can be daunting for middle-class families. But in-state tuition rates already offer a huge subsidy not based on income. An authentically progressive program would prioritize the neediest. A report by the Council of Economic Advisers finds that students from low-income backgrounds tend to have more trouble than others paying off their loans. Tuition, meanwhile, represents only about a third of the educational costs New York’s undergraduates face. The first priority must be enabling poor families to send their children to college so that talented students are not trapped in a cycle of poverty.

Mr. Cuomo’s plan has a few good ideas. Students benefiting from free tuition would be required to enroll full time, which should push up graduation rates and push down student loan defaults. Mr. Cuomo also could have done much worse, by, for example, proposing a general reduction in tuition, or even waiving it entirely, for everyone in the state. That approach would have been even less targeted at the neediest end of the income scale.

But it would have been more progressive if the governor had proposed covering low-income people’s tuition in a way that enabled them to use more of the money they get from other grants, such as federal Pell Grants, for non-tuition college costs. In the interest of creating a “free tuition” program portrayed as a near-universal benefit, Mr. Cuomo did something less useful.