A country with a powerless monarch is practically no different from a republican state. Also this:
The best and the most democratic governments in the world happen to be constitutional monarchies, they aren't the best because they are constitutional monarchies. Big difference.
In fact, they are still monarchies today only because they became good enough to not have enough public outcry for the odious system of monarchy to be overthrown.
I meant one wherein the monarch has actual power, as specified.
You mean the elected monarchy that was being discussed above? It's not a terrible idea, but I suspect it would be prone to voter disaffection over the lack of control over the executive and corruption. There's not really any data to back that supposition up though, due to the lack of elected monarchies.