Noble/Royal birth counts for nothing in Tower hierarchy anyway. As Moiraine's and Elayne's cases have rather shown, the more power you could wield outside TV because of your birth, the more likely you'll have to fight off AS "suggesting" to use you, so you better pray to be near the top and only have the Hall, Head of Ajah etc. who can order you around. It was the case for Moiraine, Elayne and Kiruna. Even Kiruna's strong enough not to have sisters above her that met RJ's required strength gap to be able to boss her around (Cadsuane and the wondergirls excepted).