Choice of multiplication polynomial in Rijndael s-box affine mapping
As I have duplicated your question by mistake and non of us have had an answer, I request help to the authors to know why those parameters where selected like that.

The affine transformation is a vector space operation $(\mathbb{F}_{2})^8$, and the simplicity comes from the fact that, from the bunch of possible transformations the one used can be also described as a product in a polynomial ring modulo $x^8+1$.

Above the criteria that the matrix (or the multiplicand constant in polynomial view) must be invertible and the vector (or the addition constant) has avoid fixed point neither opposite fixed points, they have simply picked some from the set.

The timing feature is useful when the S-Boxes are calculated on the fly, but with them pre-calculated the difference doesn't matter (I think).