"Of course we don't have those worries today, because we are going to install democracy. and if those factions want their own democracies, well, tough noogies."

In a democracy they will have their own democracies. What you are saying is similar to saying that members of the EU won't have their own democracy. The exact power of the federal govt vs state govt is still an ongoing "debate" within the US. There is no reason that Kurds couldn't be one or more states within the country of Iraq. They can be independent states just not Independent States. And though we don't want to encourage the idea, there is possiblity that a democracy can separate- such as what the French Canadians are attempting to do. Generally speaking it's a bad idea (see American Civil War) but possible.