Hope you enjoy waking up at Miraak's temple.

But seriously, why?

Because Solstheim is under the influence of Miraak so long as he controls the Standing Stones. Once the mind is idle or the player comes in direct contact with the Stones, then the Dragonborn can succumb to his Bend Will as well.

And I suppose there's no other way to take his influence off without being Dragonborn?

Well it just happens when you sleep or directly interact with the stone.