On the other hand… several Muslim theocracies are currently operating right now, and those theocracies strongly believe that the entire planet should be subject to Islamic religious rule.
Based on... wait for it... mostly, the exact same Scriptures. Plus a famous little corrective coda of course, but the Holy Qur'an does not
add in the heavenly endorsement of kingship, if anything it mediates it slightly by introducing the concept of ijna, consensus-building, to its portrait of a just king. No, Muslims are not monarchic because the Prophet (pbuh) invented kings. Islam is monarchic because Abrahamic religions are ALL monarchic, and they all tell the same stories about Abraham and his descendants to justify the rightness of that shared institution. The Hebrew God, who became in time the Christian and Muslim god, has never once offered to share power with mortals. Human authority is permitted only insomuch as the divine will is being communicated through it. Read your Bible, sometime! You'll be surprised how little of what the book says resembles what Christians claim to believe.
Mind you, concerning your portrayal of the present, I am not aware of any living Muslim state that invests all political and religious authority in one monarch. Like the Christendom, the Dar al-Islam has struggled to convince any modern populace that an unchecked autocrat is safe or desirable. Republics may not be Biblical, but they are very, very popular in our century.