Besides what was already said, I'd like to add that with only a few exceptions (most notably Japan and to a lesser degree the Netherlands, I believe) most constitutional monarchs even pay taxes on their private income.
They usually receive some kind of stipend/grant as a sovereign which is not taxed. But what they gain from "extracurricular" activities is fair game.
And I think it is worth keeping in mind that a lot of the trappings and estate of a monarch would have to be upkept as part of the cultural heritage and national prestige anyway.
So between paying for a museum/cultural heritage site and letting someone who is essentially a paid actor who got the job through their parents live in there, why not.
And you can never underestimate the soft power a well-liked sovereign can have as a symbol and tool of population control. If the personification of your state talks to the people, many listen.
In international relationships, a monarch can be a soft diplomat and fulfill the role of someone who is at a special remove even from other statesmen and can do and say certain things in certain ways.
I reckon we have reached that state for a long time.
The vast majority of people would have a pretty hard time without food logistics, utilities, medical treatments, pharmaceuticals. The list goes on.
All of which are provided by corporations of some form or another.
Something something about civilization being 5 warm meals away from collapse.