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With any POD before present-day, have a present-day world exist where no one takes monarchy seriously anymore and it is a defunct and archaic system of government.
No hereditary or elective monarchy may exist in any way, this includes 'monarchical' diarchies, triarchies etc. The only 'monarchy' that is allowed is basically a republic whose head of state is called by a monarchical name, but is elected by direct popular vote. Also no countries are allowed to have official nobility.
Not sure how difficult this would be, but I made it an AHC.
Vatican City is pretty impossible as a republic (a democratically elected pope? by all Catholics?) so I think it would not have to exist. It's both a monarchy and a theocracy so try to not have it exist.