That richness does not have to do with monarchy or republic, it has to do with stability. For the same reason Iraq was rich in the 70's (stability), I thought Libya under Gadhafi was no monarchy.
By coincidence the monarchies were allied to the US whilst the Arab republics were mostly with the Soviets, Americans won so the monarchies remained secure. Yes Kings/emirs are dictators.
The difference between monarchies in the Arab world (the first attested monarchs in world history can be found in our lands and also the oldest noble families - a testament to how strongly ingrained a monarchic/tribal system is in our lands) is that they are standard-bearers of tradition, religion and have legitimacy through an ancient connection to their land and people and a several generation long history of ruling. Including a tribal connection and having received bay'ah from all leading families, clans, tribes and leading circles in the society. Again a thing that has been the case from generation to generation in those circles be it in the military, clergy, business community etc.
They are mostly highly-educated and serve the country and people first and foremost as otherwise they risk losing their throne. All the military/populistic dictators in the Arab world since WW2 have largely failed tremendously because they were mostly from the lower classes and came to power to serve their own interests and that of their family because they knew that their rule would be temporary. They could only gain legitimacy through sheer violence, intimidation etc. as time was not on their side. They solely consolidated their power through violence, intimidation etc. You could argue that royal families did the same initially (however most Arab royal families that continue to rule today were elected by the people as represented by the leading tribes and leading communities and through military might against foreigners thus giving them legitimacy naturally - example being Napoleon) but it occurred so long ago that it is no longer relevant. Now they rule based on merit.
The Al-Assad dynasty in Syria is actually a monarchy (a young one though) that just uses the title president instead of Malik, Sultan, Emir, Sheikh, Imam etc. which is also why Al-Assad has managed to remain in power (due to the network of loyalties that he inherited in all sectors of Syrian society) despite everything that has gone on in Syria. Not only that he has attached his rule to an ideology (Ba'athism). An alliance that has lasted 40 + years. Saddam for instance on the other hand was a villager and a son of shepherd who left his mother shortly after his birth if I recall. He only knew power and was only loyal to power. It took him years to establish a network so it could even become possible for him to pass the throne to his two sons. Back to Bashar, had he been an ordinary person who took power in 2000 without any family history of ruling, he would have been toppled long ago.
For Western democracy to gain a foothold you need a generational change, an enlightened population (that actually knows what to vote for and why) and strong institutions outside of the state other than the clergy. We all know that Lebanon and Iraq are only democracies on paper like all other countries in the region except for maybe Tunisia although they have their own challenges which is logical.
Of course for a liberal conservative like me the perfect solution would be an elective democracy (if the people are enlightened enough and strong enough - I don't see that anywhere in the Muslim world currently, sadly) with an constitutional monarch that could remain as a standard-bearer and uphold the traditions and serve as a unifier in times of trouble.
I am sure that you would have preferred (looking back in history) a constitutional Iraqi monarchy (as was the case pre-1958) rather than the chaos that we have witnessed since 1958.
There would not be a bunch of useless politicians trying to get their 5 minutes of fame and selling themselves and by default their country and people to a bunch of foreigners depending on the sect they belong to and ideology.
Ask yourself why Southern Iraq is relatively safe despite all the political rivalries (very strong ones). It's the tribes of Southern Iraq that uphold the law and order.
As for Libya, we all see the results of Gaddafi's policies. That would never have happened after 2011 had the al-Senussis ruled until 2011.