I am in partial agreement with Dave. h/t does affect the wall when subject to vertical loads and out-of-plane lateral loads. Moment on the wall will have contribution from flexure, eccentricity of applied vertical load, bending due to maximum flexural displacement of the wall. High h/t will result in making the third term very large.
I agree with Dave that h/t is not an issue with a freestanding wall. Disgrgarding the h/t, design the wall first and see that h/t comes out to. Regardless of the height, you would use a 6" wall at a minimum, probably a 8". In the end h/t wont look so bad.