The trend in wildlife conservation now is the preservation and re-establishing native populations. Many times because native wildlife evolved with the habitat, they became symbiotic. Thus the introduction or elimination of a species may have detrimental impact on the whole ecosystem. Many times, we as hunters do not consider this when it comes to our priorities. I would assume the NP system has some form of evidence to show why the Goats should be eliminated. I'd also assume that even if there was a hunt allowed, that some other form of culling(helicopters) would need to be done to get them all. While many folks would do what it takes to get a trophy Billy, odds are there aren't a lot of folks that would do the same for ewes and kids. Then there's the public reaction to seeing small pretty Mountain Goat kids strapped to the top of jeeps along with social media. Hiring a professional as opposed to establishing and regulating a hunt, may be a cheaper, easier and faster way to obtain their goal. Since they weren't there to start with, and otherwise can't be hunted there, are they really taking anything away from hunters?
Here in the state of Wisconsin we are going thru the same thing with German Brown Trout and Tiger Muskies. Even tho Tigers are native to some lakes, there are really a hybrid between a Silver Muskie and a Northern Pike. Something that only occurs rarely and in specific types of lakes. Since there was demand, they became a popular plated fish in many waters. They became commonplace and then found to be detrimental to both the established native muskie and Northern populations. Same with the Northern browns and their impact on native Brookies. The state has now stopped planting any of these fish even tho many folks are opposed. Again....priorities.