It is worth noting that Yemen is an exceptional case as a relatively recently unified state. So there are huge problems the state is dealing with in terms of bringing together two separate historical political trajectories between the North and the South (of course we can see this in the civil war today). And while republican Yemen under Saleh and Hadi was extremely corrupt the Imamate monarchy that existed in North Yemen before the 1960s was also very corrupt. Probably not quite as corrupt as Saleh's republic because it was less developed, but as a result it also provided (even) less for its people.
You kinda proved my argument with the bottom sentence. No matter how you slice it. Look at the 18th, 19th, and 20th centuries, once a monarchy becomes a republic, the country becomes worse via violence, corruption, dictatorial mess etc. Personally Yemen should've remained split. After a while the monarchy part would've been a lot better off.
Also in the Middle East theres not that much difference between monarchies and most republics. Saddam, Assad, Mubarak etc all were technically republican rulers who were at no risk of losing an election and who sought to pass on power to their children. The only real difference is that authoritarian republics are more at risk of a legitimacy crisis as their legitimacy is based on popular will, which is one factor for why Arab monarchies were more resilient than Arab republics in 2011-2012.
I partially agree but here's where it raises an important question. If a republic is acting like a monarchy in terms of pasing the power and title to their children, whats the point of republics in the first place?
Also I'd be careful comparing Saddam and Assad to the monarchs of the Middle East. As much as I despise most Middle Eastern monarchs (except Oman's R.I.P. and Jordan's) they aren't as bad as Assad or Saddam. Saddam has invaded Kuwait and Iran. Assad saw fit start a civil war in his country. The only monarch who's barely comparable to them is the Saudi (their involvement in Yemen)
I think the arguments about monarchs being above party politics often obscure the political realities in a country. The truest essence of politics in a country is found in power relations rather than organized party dynamics. In countries with both a monarchy and some level of representative government (usually a parliament) the monarch can frame himself as standing above political disagreements, but this also has the effect of making the monarch seem above politics in general. This is very often done to mislead a monarch's people as his job is inherently political as a head of state. I see this really clearly in Morocco where the King allows for organized political parties but retains almost all of the countrys political power. In these cases the representative parties are just used as scapegoats to distract from the real holder of power: the king.
So much to address:
1. I disagree with the first sentence. Monarchs must be above the party politic otherwise they can and will be seen as favouring a certain party. The optics of this would be catastrophic.
2. I only partially agree with your second sentence. The true essence of politics is policy.
3. A monarch is never above politics. They should only be above party politics. Nobody is foolish enough to believe that a head of state isn't political.
4. Morocco has the right idea (mostly). Sometimes political parties are too busy squabbling among each other that the forget that they have a country to govern. It doesn't even matter who holds power, it just matters how said person wield it.
As for Morocco, lets be honest, as of 2020 is the most stable and best run North African country. Republics showing once again that they are very much prone to fukkery and failure.
Egypt and Libya were better off as monarchies.
I'm not opposed to monarchies in every instance because countries have different domestic contexts, and what is un-viable in one might work in another. But generally I think monarchies have too much of a risk of leading to nepotism, income disparity and authoritarianism.
Here's the kicker about nepotism. Nepotism doesn't get better in a republic, on the contrary it gets worse. Think about it. Instead of the royal or imperial family looking out for each other, it's now the political 'party'. That political party could have lots of members. Each member most likely has family ranging from children, siblings, cousins, parents, grandparents etc. Do you honestly think that a party member is going to ignore them? Or said party member's family is not going to use their connections with the party to get what they want?
Here's the thing, nepotism is part of human nature. If you monarchies are at high risk of nepotism then I suggest you look up China's red princes, the absolute fukkery that commie party members and their families got up to in the Soviet Union. Also the USA isn't one to talk about nepotism.
Income disparity - Many of the richest countries in the world are monarchies. Income disparity is caused by corruption. Corruption will happen regardless of a polity being a monarchy or republic.
As for authoritarianism... 20th century republics have monarchies beat many times over. The blood is still wet in many republics.