I know that it's ASB for Iraq to all of a sudden become a western liberal democracy, but with western pressure and enough money to go around, it could start to look like Morocco, or possibly Turkey or Iran pre-Operation Ajax. There would still be conflict between the monarchy and parliament over who had power, but if you can eliminate an activist military and hardcore authoritarian Arab nationalism, you can make the country much more stable. If the minority groups that inhabit Iraq (Kurds, Christians, Assyrians, etc.) feel more included and society is generally more cosmopolitan, then you have a society capable of developing into something approximating a stable, liberal society. That, combined with a nationalized oil company or heavy taxes on foreign oil concessions (capital to spend on infrastructure, healthcare and education) and an uncontested port to the Persian Gulf (Kuwait or Basra), will make Iraq a much more attractive location to base the regional headquarter for foreign firms than one of the closed, repressive oil sheikhdoms.
I generally agree with you, except that I wouldn't call Jordan, Morocco, or TTL Iraq "democracies". Sure, they're economically Liberal, and much more politically Liberal than say, Saddam-era Iraq, Syria, or pre-2011 Egypt, but that's not an especially high standard. Jordan-the most likely model for a Hashemite Iraq-is still, at heart, and authoritarian system where the royal family and a few allied tribes monopolize political power and most of the higher echelons of the military and bureaucracy, and where the parliament has heavily "influenced" elections and just as much power as the royal family is willing to give it.
Furthermore, Hashemite Iraq would have something Jordan doesn't have to deal with in large measure, namely religious and ethnic sectarianism. We can only speculate as to how, once blessed with reams of petrodollars, they would handle it-but look at Jordan, which gives disproportionate political power to pre-1948 residents and largely shuts out Palestinian-Jordanians, even though they're a slight majority, or Bahrain, where the Sunni minority hogs political power and oil wealth, and prefers to give jobs to foreign Sunnis rather than its own Shia majority. By the 1990's, I think its fairly likely that a Hashemite Iraq would be a society where Sunni Arabs were on top, non-Muslims (Christians, Yazidis, the remnant Jewish population) were just a step below them, and Kurds and Shia Muslims were very much on the bottom-with many probably living in significant poverty. Sure, it would probably be heaven compared to OTL Iraq, but it certainly wouldn't be, by any usage of the word, a "democracy".
Another possible PoD that would be even better would be butterflying away the establishment of Israel. The reaction in Iraq and much of the Arab world to the founding of Israel was to expel their entire Jewish population, which made up a significant portion of their merchant class and intelligentsia. Keeping the largely assimilated Jews around would make Baghdad, 40% Jewish at points in the 1930s, a much more prosperous city.
Well, at risk of offending all our board's Israelphiles, "no Israel" is probably a starting point for any TL to make a better Middle East. Without Israel, there won't be a Palestinian refugee problem, the latent rise of anti-Semitism after 1948 won't happen or will be far less (modern conspiratorial Arab anti-Semitism cribs every trope of its Western counterpart wholesale, because until 1948 it largely didn't exist), most Arab Jews will probably stay home-and as they formed a large part of their countries' middle class, Arab economies will be better. The humiliation of 1948-which discredited parliamentarism and directly led to the rise of authoritarian Arab nationalism-won't happen, and their won't be continued Western support for Israel to poison Western-Arab relations and legitimize political Islam.
