i understand what the brookings institute is and why it's going to present certain narratives that may be a little bit elastic regarding certain facts, so let's take a step back here.
let's begin by acknowledging that, regardless of the facts that followed, saddam was very useful to the united states in the 1980s, because he launched an absolutely brutal war against the iranians on their urging. now, skip forwards a few decades and realize that the geo-strategic aim of installing a shia leadership in iraq was to attempt to create competition for control over shia islam. there was no deficit of voices at the time that pointed out that this was naive. but, the intent was that iraq would compete with iran for influence and if they got into a firefight here or there, hey, nobody in the state department is crying about it.
rather, what happened was that the shi'ite leadership in iraq valued co-operation with other shi'ite powers, in competition with sunni powers, over competition with each other. oops.
so, at the time [things have changed a lot in the last year], you had americans going after maliki for not being "inclusive", which is a type of code that means to say that he's not doing what he was supposed to do. he was supposed to be fighting with iran, not working with it. in reaction to this failed policy, you've got saudi-backed militants running in, trying to take him down and put their own guy in place. of course, we blame it on him for not doing what he's told, rather than on ourselves for following through with a policy that was widely panned as naive.
so, what happens when you partition the state? what you do is relinquish the opportunity for saudi-influence in the shia areas, as well as the kurdish areas. further, you permanently move the front in the saudi-iranian proxy war away from the iran-iraq border and into the middle of iraq. that sounds like a great idea - if you're iran. it doesn't sound like such a great idea if you're saudi arabia.
the only way the saudis can regain their influence is if they put a sunni back in charge of a unified state. for that reason, partition will remain anathema to us policy - it would be forfeiting the most valuable parts of iraq to iran.
so, how do you fix this, then?
well, at the moment, it appears that the saudis have settled upon ethnic/religious cleansing as the preferred solution. there's obviously some problems with that tactic; although, if it continues, the harsh truth is that it may do the job.
personally, i'm in favour of regime change in saudi arabia followed by the saudis relinquishing their desire for control, but that's easier to suggest in the abstract than it is to put in place.
but, i do think the analyst is at least right in suggesting that there's not an easy answer and that there's no real end to this conflict in sight.