The Genovese family is too secretive
They have always been underground, now with the current state of LCN, and the fact that L.E. does not have programs like the "Top Echelon Informer program" lastly, the FBI cutting down their resources, one more thing there hasn't been a high ranking defector in the Genovese family is a very long time.

The bottom line is the gov"t has no idea of what's going on inside the Genovese LCN family.