It probably makes more sense if you think of matrices as n-dimentional arrays: sum eliminates the n-th dimention, insert and delete increase or decrease the n-th dimension size.
For example, if I have a 2-dimensional array and I insert a scalar value by using axis=0, the scalar value needs to be broadcasted to match the column dimension of the array:
>>> a = np.array([[1,2],[3,4],[5,6]])
>>> np.insert(a, 1, 11, axis=0)
array([[ 1, 2],
[11, 11],
[ 3, 4],
[ 5, 6]])