I've driven the roads in National Parks with these three lenses, Nikon 24-70 f2.8, Nikon 70-200mm f/2.8G VR II, and Nikon 200-400mm f4 VR on three different camera bodies. If you need the 14-24, you'll have time to change, but otherwise scenes can present themselves suddenly. If you find rutting elk, you'll pull over and get out, set up and shoot as opportunities present. In Rocky Mountain National Park you'll find crowds of people with coolers and lawn chairs set up where the elk rut is most active. In Denali there are fewer people, but still plenty of photographers cruising for rutting moose. In either case the animals don't pay much attention to the people. However, I was quietly waiting for a big bull moose to stand up in Denali and another photographer walked in. He waited for a while and then said he was going to make something happen. The bull went from relaxed and calm to chasing both of us out of the woods in an instant. I wouldn't be surprised to read that the other guy gets trampled to death by an animal somewhere sometime. I saw his credit on a cover photo of a charging bull moose on one of the outdoor magazines a couple of years later.
