This is a very important topic, so thanks for the post! But responding to violence with an effective "justice system" is not a self-evident description of a solution. Many Western "justice systems," most notably that in the United States, are very violent in themselves, from abusive cops, stop-and-frisk, to prison conditions and even the death penalty. These systems assume that doling out punishment is the main purpose of state-sponsored "justice," and assume (with little to no evidence) that punishment is an effective deterrent to violence and crime. International comparisons show that counties with the least violence also have more lenient justice systems, focused more on restoration than on punishment.
Replacing socially pervasive violence (especially against women) with a legalized system of violence would not be the improvement the author seeks (at least I hope not). Just as we talk about developing countries "leapfrogging" over proven but dirty development paths in the energy field (i.e. skipping coal power plants and moving straight to wind and solar in the quest for access to energy), we could imagine that in countries with currently ineffective formal justice systems, they would not need to replicate the U.S.-led model of punitive justice in order to prevent the plaque of violence that is holding back so many women. They should aim higher -- and so should the U.S.