It
is absolutely possible to have zero sideslip and non-zero bank.
Take an axis-symmetric cylinder whose longitudinal axis is aligned with the velocity vector i.e., \alpha & \beta = 0.
Rotate it about this axis and tell me you still believe what you affirm to be true is the case Milt...
People are still confusing the axes systems involved in this problem.
Aerodynamics isn't sensitive to \phi.
The state vector includes six fundamental variables none of which is \phi!
The mathematics never lies.