There is an argument to be made that not only Iraq, but the entire nation structure of the Middle East, was botched when it was originally set up by the Allies after World War I. (For an excellent accounting of how the modern Middle East was created, I encourage anyone who is interested to read David Fromkin's A Peace to End All Peace - it will astound you.) But we have to deal with the countries as they exist today, imperfect as they are. If we were to separate Iraq into more autonomous regions, the time to have done it would have been when we were occupiers. Now we're not - the Iraqi Government (another imperfect entity) is in control. So Biden's about four years too late for this suggestion to be meaningful.
But it raises a good point. Why didn't we do this in the first place, as people like Rich Lowry of National Review was suggesting at the time? I believe that it's because it would have created, almost immediately, a larger regional war. Turkey would have tried to claim the Kurdish north, at the same time the Turkish Kurds would attempt to secede from Turkey to create an independent Kurdistan. Iran would have moved to claim the Shiite south. And the Sunni middle would have been ripe pickings - they'd control Baghdad and Tikrit, but would have little natural resource wealth. Eventually, the Shia/Iran south would attack the Sunni middle to enact revenge for what the Sunnis did to the Shia during Saddam's reign. We'd be in the middle of all of it.
Thankfully, that is not going to happen. The article in The Hill does have a good quote from a Republican aide which shows just how empty Biden's victory was:
One GOP aide went further, saying that most Republicans decided against opposing Biden's plan after revisions made clear that it would not force any decisions on Baghdad. "What is the Iraqi government going to do [in response]? Say, 'thanks for the input, but we're fine'?" the aide said. The aide described Republicans' perspective as: "This doesn't really do anything, and why not let [Democrats] have it, for practical reasons."
