Maybe the best way to understand it intuitively is that the drive would actually work for a little while after you first turn it on, but as it shoots charged particles in opposite directions, it creates a field in its region of space that eventually gets strong enough to pull it backwards by the same amount that its thrust pushes it forwards. By continuing to add energy it could continue to
move, but it can't continue to
accelerate. The best it could do, perhaps, is to accelerate to a certain velocity, then turn off its generator and discharge its plates so it now has no net field, and then coast to its destination.
Probably part of the confusion here is that a dipole does have a nonzero field even though the net charge on it is zero. Dipole fields are often negligible, particularly as they fall off faster than monopole fields -- 1/r^3 rather than 1/r^2 -- but ignoring the dipole field is another familiar approximation that doesn't hold in this case.