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.
Very good point. Additionally, with insert and delete we might need to apply the rules of broadcasting [0].
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:
