What's wrong with dividing Iraq? It was the solution we used in Germany (in to an East and West plus a separate Austria), Korea (into North and South), India (into India and Pakistan (and Pakistan into Pakistan and Bangladesh)), the Soviet Union (into Russian and the CIS), Yugoslavia (into the Balkan states) among others. If partition was a good enough solution for all those states, why not Iraq?
Dividing Iraq doesn't force the various factions to work together. It only sets the stage for Balkan-like instability.
Once the militant factions are brought under control and they are forced to submit to elections and civil authorities, the situation in Iraq will improve. It might take them a generation or two, but the region will be better off for it.
As for Biden's idea about what to do with the oil, try and imagine what could possibly go wrong with the Oil for Food program, and then triple it.
You must not know any history. That's an amazing list you made. Can't imagine having the time to enlighten you.
Wouldn't the continuing conflict in evry one of those regions suggest the solution was not too good ?