There are several things which come to mind in response to your post.
First, you assume that because the kings cited in the Qur'an were prophets or appointed by prophets, that this is an exceptional circumstance, but the prophets were all sent to demonstrate the deen, and in taking upon themselves kingship, they were demonstrating a form of governance.
There are sunnahs of the prophets which are not sunnahs for us, such as fasting continuously or marrying more than four wives, but then there has to be a definite proof that such is the situation. Otherwise, it is very dangerous indeed to consider the practice of the prophets as being elevated and beyond our reach since the very essence of what they were doing is demonstrating the way for us.
This in fact happened in Madinah when one of the Companions asked about kissing one's wife while fasting. This is from the Muwatta:
"A man kissed his wife while fasting in Ramadan, and became very upset because of that. So he sent his wife to ask on his behalf about that. She went to visit Umm Salamah, the wife of the Prophet, may Allah bless him and grant him peace, and mentioned that to her. So Umm Salamah informed her that the Messenger of Allah, may Allah bless him and grant him peace, would kiss while fasting. So she returned and informed her husband about that, but that only increased him in distress, and he said: “We are not like the Messenger of Allah, may Allah bless him and grant him peace. Allah makes halal for His Messenger, may Allah bless him and grant him peace, whatever He wishes.” Later his wife return to Umm Salamah and found the Messenger of Allah, may Allah bless him and grant him peace, with her. The Messenger of Allah, may Allah bless him and grant him peace, said: “What is the situation with this woman?” So Umm Salamah informed him. The Messenger of Allah, may Allah bless him and grant him peace, said: “Have you not informed her that I do that.” She said: “I have informed her and she went to her husband and told him and that increased his distress, and he said: “We are not like the Messenger of Allah, may Allah bless him and grant him peace. Allah makes halal for His Messenger, may Allah bless him and grant him peace, whatever He wishes.” So the Messenger of Allah, may Allah bless him and grant him peace, became angry and said: “By Allah! I have the most taqwa of Allah of any of you, and I am the most knowledgeable of you of His limits.”"
There is no evidence of the kingship mentioned in the Qur'an being exclusively for prophets alone or those appointed by prophets, because that would need some clear statement to that effect. None exists.
Of course, we are already loaded with preconceptions, and we are largely arguing about our preconceptions, for example, what we think kingship is.
Monarchy means simply rule by one man, and as Philip Blond said in his radio talk, we are always ruled by one man or woman, whether a king, prime minister, president or dictator.
King may derive from two possible Germanic roots: to know (ken) or to be able (can), and these are also qualifications for a khalifah.
We have a daft image, largely from the forces that work constantly to prevent the re-emrgence of kingship, of absolutist monarchs ruling imperiously and arbitrarily, but any serious historical study will find far more consultation taking place around monarchs than does now in Congress or the British Cabinet.
However, the most misleading thing in your article, Sidi Isma'il, is that of taking philosophers' discussion of these matters too seriously, for these things proceed by the realities of power and politics, not by the wishes of philosophers, who are largely a helpless lot. Indeed, because of their distance from the seat of power, they have often quite mistaken ideas of how these things work and are merely whistling in the dark.
Of those who should be paid attention to, certainly Ibn Khaldun is one, simply because he was rarely very far from actual power and history in the making.
Let us be clear. If we talk of monarchy, there is no sense of a king being above the law. Whatever form of rulership we have, rulers are only put in place to put the law into effect.
As for consultation, Allah commands the ruler to consult, and He commands that when he has made up his mind, he should rely on Allah. It is not, as mistaken modernists insist, that the ruler is bound by majority decisions. This is wrong by the text of the Qur'an and by the practice of the khulafa, although there is sometimes wisdom in the view of a majority of knowledgeable people. As to the majority of the masses, that is completely irrelevant, since repeatedly in the Qur'an, Allah, exalted is He, says words to the effect: "Most of them do not believe," "most of them do not know," etc. Majority in the political sense as used today is certainly no proof.