> What exactly is the justification for having those tasks, if they're deemed necessary, executed by some hereditary, secretive, uber-wealthy family rather than by someone who is actually a civil servant?
The easiest ways to corrupt someone are offering them wealth, opportunities for their children, or a popular reputation; the royals are relatively immune to all of those.
> offering them wealth, opportunities for their children, or a popular reputation
The government literally pays them and promotes them as a symbol of the nation - how is that not offering them "wealth, opportunities for their children, or a popular reputation"?
The easiest ways to corrupt someone are offering them wealth, opportunities for their children, or a popular reputation; the royals are relatively immune to all of those.