There are herd control, or cull hunts by helicopter, but no game hunts - and shouldn't be.
I agree totally - organised culls when animal numbers are high is completely justifiable. And if populations exceed a set threshold based on conservation values for that area etc, then a cull is necessary. But these culls are done by professionals, and not by paying Clients. And our govt refers to these as "management culls"
"Heli-hunting" on the other hand is purely for trophies and our New Zealand regulatory bodies are trying to dress heli-hunting up as legitimate form of "hunting"... as if it's part and parcel of the sport
