Can we not say: "The dimensions are the same but the units are not."
We can (there is an existence proof in this self-answering question),
but where is the value in doing so? What do we learn about Nature by
doing so? In what way will we facilitate learning by doing so? The
only function of such an addition to the curriculum would be to give
us one more item that could be included on a multiple choice test.
Nature abhors multiple choice tests! (So do I, and I administer them!)