Nope, nothing I suggest is close to a monarchy; I'm very against such an anachronistic institution. You've gone out of your way to make a ton of ridiculous assumptions to build a worst case scenario here.

But, yes, religious oppression to a point is a good thing. At a minimum kids should not be allowed to be indoctrinated.

More power to act unilaterally does not equal complete power to act unilaterally i.e. a monarchy.

A qualified pool would be based on education, not heredity.