Study after study has shown that speed makes a huge difference in the rate of death for pedestrians. At 20 MPH, there is a 5% fatality rate; at 40 MPH it is as much as 85%. (source) This doesn't even take into account that a lot fewer accidents are going to happen when drivers go more slowly. In London, the rate of deaths and injuries dropped 46% when the speed limits were lowered.
Now Mayor de Blasio has managed to get Albany to agree to lowering speed limits in New York City to 25 MPH. Timing on lights will be adjusted accordingly. This is a switch; according to the New York Times, lights were set for maximum throughput. The last time I was in a cab in New York, it flew up Park Avenue at about 60 MPH and never got a red.
Many activists would say 20 is plenty, but 25 MPH is certainly a start. More at Transportation Alternatives.