I expect to be downvoted for this but I think there is an appeal in an institution that dogmaticaly upholds a "higher" ideal of human behavior. They try to provide us with an example of how a hypothetical family with essentially unlimited resources that is born into this world with a social duty should theoretically behave. They also show us constant examples that human emotions are a factor regardless of your socio-economic situation. This provides the layman with an answer to the question "what would I do if I won the lottery and was instantly vaulted into the highest social circle?" Would you use your influence for the good of the people while maintaining a scandalous affair? Would you fall into the same emotional traps as the royals?

I think it's an interesting social experiment that may be worth the cost it requires to maintain.