This understanding is completely outside of actual reality. The statement "Monarchy is superior to democracy in a very important way" goes on to explain why you believe the monarch has a greater incentive to avoid wasting the lives of his citizens. This isn't even close to true. A monarch who loses 1% of his "wealth" in the form of dead people still has the other 99%. A President can lose his job, his wealth, and his personal power for less.
A president is incentivized not to put upon the people more than they can bear with the understanding that all they have to do to be rid of him is check a different box next go round. A monarch faces the same risk but only if the anguish of the people is enough for them to spend copious amounts of their own blood in violent revolution.
This difference in resistance is the dominant difference in motivation NOT a proprietary feeling towards a kings subjects. This is well born out by an ocean of blood spilled foolishly by monarchies through history. I don't misunderstand you. I don't think you have properly understood history.
Next this doesn't even work out if we replace the monarch with an automaton which faithfully executes economic theory.
A monarch of 100M people might spend 10,000 people for some end that on net increases his wealth whereas a president of 100M might find the rest of the people so appalled at the 10k corpses that they vote him out of office.
If you look at how monarchs have actually and in fact spent the blood of their people historically we wouldn't have to argue theory. Throughout history monarchies have spent their people liberally in proportion to their ability to do so. You can look at recent history at a bunch of nations that are still technically monarchies you will note that their period of moderation directly coincides with the waning power of the very actor you claim somehow serves to moderate the state.