Of course there hasn't been a High Queen of Ireland. The High King was
wedded to Lady Sovereignty, sometimes symbolised by a white mare with whom he
mated as part of the ritual. A little awkward for a woman to do. As for
Medbh, she was only Queen of Connacht, not the whole island.
According to tradition the king had to be whole of body, which is why Nuada
had to relinquish the crown when he lost his arm. This goes back to the
Sacred King concept; he had to be a perfect sacrifice if called upon for
that. Women were exempt from having their blood shed in sacrifice because
they bled monthly; another reason there couldn't be a reigning High Queen.
This prohibition, although ancient, might have been one of the reasons
Mathilda, daughter of Henry I of England, was rejected by the barons in
favour of her cousin Stephen for rulership of England.
Perhaps they understood PMS better than we thought they did.