Its precisely because the monarchies and their wealth were never fully destroyed in these countries.
These royals have a lot of power in their local economies because im a lot of cases they still own a shitton of estates and land (not to mention investments, connections and as you said institutions).
It is in the interest of the local bourgeois to at least support the continued existence of the royal family as that gives them potential access to these resources.
The royals also create a shitton of propaganda, so some people see them as a needed part of the countries culture or some historical artifact in need of maintaining. A "living monument" or some shit like that.
same amount as the people attacking the internet archive