They ceded their powers to their family office managers who rule by proxy, both tending to the inherited wealth and investing it so that they can live without having to do any work.
To be fair, rich or upper middle class European is probably actually a better gig than old-timey king from when they were in charge, hah. No countries want to kill them as a major political objective anymore, the creature comforts produced by modern industrialized societies are incredible if you can afford them, and even the nobility in a feudal system has bunch of stupid rules they have to follow, which we’ve just thrown out in liberal democracies.
A belief in that speech in the Iliad which justifies getting the best portion of everything at home because of one's willingness to stand in the van overseas being one example of a custom/rule which proved exceptionally stupid in the years leading up to 11 Nov 1918.
That made me realize something, those "stupid rules", specifically the ones about what is an appropriate marriage, are the reason the probably most well known Habsburg was in a modern convertible car on his last day.