If we are truly talking actually hunting mountains. Alpine, bowls, ravines, etc then a 4-500 yard shot is not far. Most of the time getting closer is not an option and changing you vantage point you will loose sight of that animal.
Climb up high, tack up some vital sized balloons on even a moderately windy day. Take a high bc rifle and a low bc rifle and let your “hits” tell you what bullet you ethically want to use. The wind is crazy variable up high.
No bigger nightmare than a poorly hit animal on the mountain. Lots of animals lost from that as the energy it takes to look for an animal on steep slopes is rediculous.
