We have professionals able to cope with they in the best public benefit.
Managing key species as a bussiness only for a minority of the society leads often to lots of money lost for all citizens. We talk of species absolutely necessary for having a healthy ecosystem.
Wolves create economic damages but also pay generously for them. They clean lyme, keep cattle diseases under control in wildlife reservoirs, improve pastures and build forests and rivers. Wolf's work literarily create entire biocenosis with decens of new animals linked.
In Yellowstone the wolf build from nothing a $5000000/year bussiness in a few years. Those new opportunities attract and fix young human population and put children in some states that need it.
Alive wolves trigger a lot of unexpected benefits for both humans and animals. We could never pay its environmental services, or the lifes of humans saved by wolves directly or indirectly