While it is true that there is no “correct” way to define which one is the multiplicand and which is the multiplier, this is besides the point. The teacher can use whichever definition desired and force the student to use this definition as well. There is value in grading a student’s ability to stick with the teacher’s definition/method.
In regard to the commutative property, first you have to settle on a definition of multiplication, and only then can you establish the commutative property using that definition. The definition of the operation is the foundation on which the property is built. There is no point to having a commutative property if you are going to create an ambiguous definition of multiplication by including the commutative property within the definition of multiplication itself.