Yes. IMO, Aoudads (Barbary sheep) should be eliminated from any mountain ranges historically holding Desert Bighorns. The two don't co-exist well. Aoudads, being more prolific and better adapted to arid conditions, due to their evolution in the super-arid Sahara desert, outcompete Desert Bighorns and dominate available habitat.
In West Texas, the Feds with Big Bend National Park are finally coming around to a view that exotics, like Aoudads, need to be controlled if they are displacing native animals, like Desert Bighorns. This change, if implemented, will be departure from previous "no-kill" policies supported by animal-rights groups and others.
Aoudads are tough, wary, spectacular animals, and provide a quality hunting experience. But there are many alternative places where Aoudads can live without displacing Desert Bighorns from their native ranges.
Friends in Arizona, Nevada, Utah, Colorado, etc...... kill any Aoudad you see before they take over the country. Once established, they are very difficult to control.