No reason to me to have this restriction
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“add” means you add something to the triad and don’t add anything else. “Cadd9” means: Play c-e-g and add d, but don’t use the 7 (or anything else). So “Cadd13” means: Play c-e-g and add a, but nothing else.
(In fact you wouldn’t use this, because without having a 7 in the chord you wouldn’t use 13 but 6. So if you really want to have c-e-g-a and nothing else you could use Cadd6 – but I haven’t seen this in any context.)
So using the “add” bans other additions to the triad. Cb9/add13 would be a contradiction in terms.
so how would we notate a chord with both a b9 and a 13
i’m specifically trying to do a Ab7(b9)(13)- how do you do that -without- adding an 11 also