Kingship is unstable, while some kings may govern with respect to laws, there's no guarantee the successors of a good king will be good.
It's far better to run government with limited powers checked and balanced. The recent SCOTUS decision giving the President immunity from American law in official presidential matters directly usurps the Constitution and is one step closer to dictatorial rule.
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Equality under the law ensures the principle that all people should be subject to law to ensure good and decent lawmaking. No one wants to make laws unfairly when they have to live by those same laws. Nothing flourishes quite like equal treatment under the law.