A reasonable mental model for count_nonzero is (x != 0).sum(...). But if fails in this case:

>>> x = np.arange(3)
>>> (x != 0).sum(axis=())
array([0, 1, 1])
>>> np.count_nonzero(x != 0, axis=())
2

axis == () should mean (x == 0).astype(int)