Eskimo is out of favor for the same reason oriental is. It is a generally non-descript blanket term for a huge range of people that generally don't care much for each other. It is not a term that any of them would use to describe themselves.
The other (real) reason is for the authoritative left to attempt to seize control of language; or at least destabilize rival groups use of it.
They do use it. I've seen that.