Other libertarians supported the war in Iraq because they viewed it as part of a larger war of self-defense against Islamic jihadists who were organizationally independent of any government. They viewed radical Islamic fundamentalism as resulting in part from the corrupt dictatorial regimes that inhabit the Middle East, which have effectively repressed indigenous democratic reformers. Although opposed to nation building generally, these libertarians believed that a strategy of fomenting democratic regimes in the Middle East, as was done in Germany and Japan after World War II, might well be the best way to take the fight to the enemy rather than solely trying to ward off the next attack.
Moreover, the pro-war libertarians believed there was "legal" cause to take military action against Saddam's regime--from its manifold violations of the ceasefire to firing on American planes legally patrolling the "no fly" zone and its persistent refusals to cooperate with weapons inspections. Saddam's regime was left in power after its unprovoked invasion of Kuwait on these and other conditions that it repeatedly had violated, thereby legally justifying its removal by force if necessary. Better to be rid of Saddam and establish an ally in the war against Islamic jihadists in the heart of the Middle East, the argument goes, and then withdraw American troops.
As to the first paragraph, I can only say that a democratization and liberty rationale is still no decent reason to invade a country and inflict hundreds of thousands of casualties on that country's citizens. Some supposed desire to encourage the spread of "liberty" does not alone justify an invasion of sovereign nation that poses no threat to us. In fact, it's this sort of magical thinking that results in botched occupations following such invasions. The "mismanagement" that Sullivan laments follows naturally from wing-and-a-prayer foreign policy.
Secondly, there was no "legal" rationale for invading Iraq, as Barnett admits by putting the term in quotes. Saddam's numerous violations of UN resolutions were no more than irritating and harassing actions that in no way threatened the success of the containment operations. They certainly provided no justification for invasion, "legal" or otherwise.
Honestly, I don't know what a "rational" interventionist is, but that community is not composed of those who supported the invasion of Iraq, except perhaps in the sense that they "rationalized" the invasion with tenuous reasoning. That Iraq has become a hell-hole is not really a huge surprise to those of us who did not rationalize that country's invasion, but I suppose we can hardly expect to take any credit for that. Instead we're left to fume as those who supported the invasion (but not necessarily the Bush administration in general) search their souls sadly and sincerely for the error of their ways.