actually our military developed rather close ties to the Iraqi military during the Iran-Iraq war. We discreetly chose sides and it was with Iraq.
Libya was always an ally of Iran and also a proxy of Russia, hence its Russian radars and military equipment. Iraq had mixture of French Chinese and Russian equipment. the French being the most capable
Many Iraqi officers - especially Air Force officers- were trained in France or by France. There were also ties between the middle and upper classes who dominated the Iraqi civil service and military officers and oil industries, and the Brits, from colonial days.
I don’t think Qaddafi or his people have any similar ties with their former colonial masters in Italy.
Unlike Iraq, there aren’t going to be too many Sorbonne and London School of Economics and Oxford and Sandhurst educated Libyans to write a new consitution when the smoke settles.
There really are few parallels between Iraq (fairly well educated and western-exposed, mostly sunni, not fundamental muslims) and the abysmally primitive Libya - except both were oil producers and both were ruled by despots. Let’s hope we don’t develop another parallel by getting involved in a protracted Libyan civil war - that actually will be necessary to sort out the next generation of power players in the Mahgreb.