Probably both.
But is it destabilizing? Not necessarily – when Parliament decided that it got to decide who the King of England was rather than going by primogeniture, the British monarchy didn’t destabilize in the long run, it just changed the principle by which succession takes place.
So in this case, subtly, the Great Council was establishing a precedent that, in the case of a disputed succession with a number of subpar candidates (a baby, a maester, a youngest son, etc.), the support of the majority is what makes the king legitimate.