Because of the vast distances involved, and the climate, there are really a lot of different ways to look at the way perdiem is, or should be handled in Alaska.
When you are paid by the government to do government work out of your home, that’s income. It’s like “telecommuting.”
If the per diem is part of the compensation of your employment when you are in fact, home, it’s income.
The Government of Alaska could make it a condition of the job for the Governor to reside in Juneau during the term of office. AFAIK, there is no such requirement.