Another related question: Would this character also be able to fly? If not, they'd either fall through the floor (if still affected by gravity) or be unable to move (if unaffected by gravity). Another concern is how they breath, since they'd be out of phase with the air that was just filling their lungs (unless they could also phase that, but then there would be the problem of getting more).

I'm not trying to shoot anything down here, just presenting potential avenues of limitation for the power.