Greetings in that Divine and Most Precious Name of Our Lord and Savior Jesus Christ!
The problem with systems of elected officials is that you might elect someone who stinks. The problem with a monarch who stinks is that you can't get rid of them until they die. Something to think about.
History is wrought with deposed and dead kings who the people were displeased with. There is a world of difference between power (which is fleeting) and authority.
To the OP:
Part of Orthodox ontology is a submission to God, and God's authority. We submit to the Church because she is appointed by God. We submit to the government for the same reasons. When the government is a democracy, it is run by the people, and in this regard, the whims of the people (influenced by Sin) become the government, forcing us at times to submit to sin. True, in a monarchy we have the same problem, because the king is a person to, but the difference, submit to a conflicting plurality of sin (i.e., majority rules) or submit the sins of an individual or small group. Plus, it is easier to convince a small group of leadership to follow the Spirit than a large mass.
Remember, monarchy only has actual power because people buy into it. Power is only given when people accept it. No king exists by their own might, rather, people willingly accept kings for a variety of reasons. So, there is still a hint of democracy even in monarchy, the difference is, the king serves as a kind of middle man between the changing whims of the common masses. In Rastafari, we call democracy demonacracy because we feel it gives unnecessary power and influence to diabolical forces who like to whisper into peoples hearts morbid suggestions.
What ever government is there, is put in place by God, and I accept them all, and pray for the presidents as much as the kings, but I feel more comfortable submitting to a king than a "democratically elected" leader, who must yield to shifting opinions like the tides of the Sea which the people are rightfully thought of in prophecy, turbulent, churning, instable and yet also a massive force of nature to be reckoned with.