That education system was modeled after the English system with a few influences from the Soviet Union mainly (socialism basically). There is no evidence of the Hashemites not being able to do those reforms when they did so in Hijaz earlier (a pioneer in terms of secular rule, press freedom etc. in the Arab world and that was 100 years ago) and Jordan during that same period. They were just influenced/dominated by the wealthy Sunni political elite and the Sunni landlords who wanted to regain power by keeping the majority Shia poor. The Hashemites wanted to do a lot of reforms but the people nor the country were ready for those reforms nor were Iraq in the 1930's, 1940's or 1950's any worse on a political/state level than other ME countries. In fact it was quite good despite the big complexities of the country.
Anyway the young King Faisal barely had any power. The real power during the reign of King Faisal II and King Ghazi was found among the military (labelled after the English model) and politicians and prime ministers such as Nuri as-Said (especially), Rashid Ali Al-Gillani (himself from a well-known Sadah family), Al-Midfai etc.
The alternative to King Faisal bin Hussein was this man below and he was from a Sadah family too:
Abd Al-Rahman Al-Gillani - Wikipedia, the free encyclopedia
in any case there is no excuse to what those uneducated masses did in 1958. The Hashemites never committed any crimes and wanted the best for the country and besides that then NUMEROUS branches of their family had been living in Iraq since the time of Hasan ibn Ali (ra) and Hussein ibn Ali (ra) and obviously still do to this day in great numbers. The Makkawi Hashemites themselves intermarried with people from what is now Iraq before they ended up in Iraq.
Anyway people can choose whoever should rule them but defending those massacres is wrong. Tell me, what did a 22 year old King Faisal II do wrong for him to be gunned down cowardly before his wedding and the executioners not being able to look him in the eyes when they executed him?
Excellent report by Al-Sharqiya that depicts the historical reality of the sole survivor of the 14 July massacre in 1958:
Of course I can never accept those savages for more than they are.