When the state Legislature last month failed to extend a program that used speed cameras around schools, some politicians, including Gov. Cuomo, said the city should at least install traffic lights near them.

But a new study shows that all of the most dangerous intersections near schools already have traffic lights, so the proposal wouldn’t increase children’s safety at all, according to traffic advocates.

The fall-back plan doesn’t “seem to offer more protection for students at the schools we identified,” said Steven Kalifowitz, president of data-cruncher Web site Localize.city, which compiles public stats to offer neighborhood profiles.

“I hope Albany can take a closer look at our insights and craft legislation that will measurably decrease the crash rates at these intersections,” he said.

The intersection closest to Manhattan Village Academy at West 24th Street and Sixth Avenue is at the top of Localize’s list of the 20 most dangerous intersections near city schools. It has traffic lights — yet still saw 31 pedestrians and 21 cyclists injured between 2013 and 2017.

The intersection of Jerome Avenue and West Fordham Road, which is near PS 33 in The Bronx, was the site of 39 hurt pedestrians and five injured cyclists in the same period — and there’s a traffic light there, too.

Transit advocates say Localize’s data is more proof that legislators need to get back to Albany before the end of July, when the current speed-camera legislation expires, and renew and extend the program.

Internal squabbling led lawmakers to table the bill to extend a 4-year-old pilot program that installed 140 ticket-issuing cameras around city schools. The proposed legislation would have brought the total number of cameras to 290 citywide.