I feel like there are a lot of posters shitting on ceremonial monarchs. So, can I just say I think that ceremonial monarchs are at least better than no monarch at all, and that I think they at least play an important ceremonial function?
I think there's still an important political function of them in recent times. Although rare, you have the odd cases of people like Juancarlos stopping another Spanish civil war, King Albert II running Belgium, Grand Duke Henri courageously standing up for his religious role (even though he ultimately failed in this regard in the end), etc.. Politically, they have the role of, "The last wall of defense," or "The ultimate backup plan."
More important is ideological. Monarchism is antithetical to the idea of egalitarianism and that people are necessarily equal. I think there's a lot to be said about the importance of that idea, keeping it front and center, and at the very least maintaining it as a counter-current to the current Marxist sociopolitical trends. When you have a monarch, even if they are just "ceremonial," it is like having this constant subconscious articulation of that idea presented to the public.
Pic very much related.