She's the mother of dragons due to her bloodline. It's her bloodline that gives her claim to the throne of Westeros. It's why Robert wanted her assassinated. In any feudal society bloodlines are important. As OTC said, when bloodlines get ignored, new myths need to get created to support why the new dynasty should be ruling. It is much more than "just whoever gathers enough allies and kills enough/the right people." If you do not think bloodlines are important within this diegesis you seriously are not getting much of this even if your whole view is shaped only by the HBO show.