Since I said the Alaska Airlines Eskimo is stereotypical, I also should say how to fix it.
Apparently Alaska Airlines used to use a variety of images on its planes. Here are some pictures of them:
Alaska Airlines Retro Paint Scheme
I like the idea of using a variety of images. Here's how it could work.
Natives make up about 1/6th of Alaska's population. So use an Alaska Native on one of every six planes. Choose a face that doesn't require a parka to identify it. Alternate between men and women, elders and children.
For the other images, use the gold panner, the Onion Dome Church, or the raven symbol. Use animals: an eagle, bear, wolf, caribou, seal, or whale. Use natural features such as Mt. Denali, a pine tree, a glacier, or an aurora borealis. Use one of Alaska's tourist attractions--assuming the state has any attractions that I haven't mentioned already.
This would put Natives in their proper place as one aspect of Alaska's history and culture, but not all of it. And certainly not a stereotypical representation of it, as if Alaska has nothing but Eskimos in igloos.
Of course Alaska Airlines won't do this. It probably wants a single image to brand the airline in people's minds. It'll probably stick with its Eskimo as long as possible.
And if the airline ever decided to get rid of it, people probably would force it to keep it. You know how people love their mascots. While they fly over and ignore the real Inuit, they want their lucky Eskimo charm to accompany them.
Anyway, don't say I never present solutions to the problems I discuss. It's not my fault if people can't or won't implement my solutions. I guess they'd rather stereotype than switch.