To be honest, I couldn't really care less about the figure head kings or queens of the world that aren't doing any harm, as an American I have no say and am unaffected (Outside of annoying news about royal families I don't care about), and would not care much if they were removed or kept in 'power'.

That aside, your claims don't hold for at least one such ruler, at least not in the way you present it. Queen Elizabeth is also the Supreme Governor of the Church of England. It's quite obvious where Queen Elizabeth can claim her power in that regard, with it coming from God. Churches don't operate claiming that their legitimacy comes from the people, that'd be odd to base a religious organization on a secular foundation.

To say it's outdated doesn't quite make sense. The foundation of the Church of England was it being established by King Henry VIII, the crown had created it and was highly tied together with it, it'd be odd to fully part the two from one another. To say it's redundant also doesn't make as much sense in the same regard.

Although the monarch's authority over the Church of England is largely ceremonial, the position is still very relevant to the church and is mostly observed in a symbolic capacity.