They don't have absolute power. Haven't had since long before George III.
Modern monarchies play a constitutional role as the ultimate guarantor of the rule of law. If you get a nutty populist as political leader, a monarch is a backstop who can dismiss them if they get out of control.
It's a quirky role but provides comfort occasionally.
In the US, the Supreme Court has some of the same functionality, but only in matters of law. In a constitutional monarchy, the military also pledges allegiance to the crown. Monarchs have an interest in the long term stability of their realm.
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