I know that we don’t need to wear tefillin on shabbos and Yom Tov because we only need 2 of the 3 signs to be fulfilled (tefillin, bris mila, And shabbos/ Yom Tov), and since we already have a bris mila and it’s shabbos, we don’t need to put on tefillin. (Source needed)
But why don’t we anyway? Just because we don’t need to put tefillin on, doesn’t mean we can’t.
Note: please do not answer that it was never done and therefore it was accepted as Halacha/ it became muktza because it has no use, as it could have been put on when this heter was first made, and through that become a minhag (think ma’ariv).
Please keep in mind that there is an argument in the Gemara whether tefillin is a mitzvas asei shehazman grama or not (kiddushin 35a), so according to one opinion, we should put tefillin on on shabbos, and the minhag (or Halacha) not to was codified since the Gemara.