You can get bogged down in genetic lines and inheritances, but at the end of the day the whole thing boils down to Varys' riddle about power.

“In a room sit three great men, a king, a priest, and a rich man with his gold. Between them stands a sellsword, a little man of common birth and no great mind. Each of the great ones bids him slay the other two. ‘Do it,’ says the king, ‘for I am your lawful ruler.’ ‘Do it,’ says the priest, ‘for I command you in the names of the gods.’ ‘Do it,’ says the rich man, ‘and all this gold shall be yours.’ So tell me – who lives and who dies?”

Power lies where the people think it lies - and in KL right now, you'd be hard pushed not to believe it lies with a woman who just murdered everyone else in the city with any claim to power in one fell swoop.