While I do believe in well regulated hunting as an effective conservation tool I don't believe that is what is present in Africa. 98% of the tourist economy in Africa is tourists going to see the wildlife not to hunt and of that 2% very little of the money goes to the local villages. It is mostly paid to large businesses and government agencies who may or may not hire locals.
But realistically I don't think that hunting will cause or save elephants from extinction, poaching and loss of habitat are the big killers of the African elephant and will have to be addressed if these animals are going to survive. I hope that those who seem to want elephant hunting to continue will do more to make it beneficial for the elephants since the status quo does not seem to be effectively managing elephant populations.
I think you are wrong, they seem to be pretty effectively managed in areas that allow hunting as populations have shown stability and even increases. It is in the areas with no legal hunting that poaching is rampant and the populations are being decimated.