As far as annexing Iraq concerns, I think you underestimate just how "heavily" we would need to influence Iraq. For Iraq to finally stabilize, their infrastructure needs to be rebuilt and Iraq isn't up to that task:
* According to a March 2011 report by the UN's Inter-Agency Information and Analysis Unit, one in five Iraqi households use an unsafe source of drinking water, and another 16 per cent report daily supply problems. The situation is even worse in rural areas, where only 43 per cent have access to safe drinking water, and water available for agriculture is usually scarce and of very poor quality. These facts have led more Iraqis than ever to leave rural communities in search of water and work in the cities, further compounding already existing problems there. The UN report states: "Quality of water used for drinking and agriculture is poor, violating Iraq National Standards and WHO guidelines. Leaking sewage pipes and septic tanks contaminate the drinking water network with wastewater. Eighty per cent of households do not treat water before drinking. Furthermore, just 18 per cent of wastewater is treated, with the rest released directly into waterways."
* Street side electricity generators are now a common sight around Iraq's capital city, where the average home receives between four and eight hours of electricity each day. Some areas, such as Sadr City, receive an average of less than five hours a day, with some portions of the area receiving a mere hour to two a day - and sometimes none at all. Many people opt to simply pay private vendors for electricity from the generators, whose owners run lines to their respective clients. Some areas of Baghdad continue to receive one to five hours of electricity a day.
* According to the UNDP, Iraq has a poverty rate of 23 per cent, which means roughly six million Iraqis are plagued by poverty and hunger, despite the recent increase in Iraq's oil exports. Iraq's Ministry of Planning has also announced that the country needed some $6.8bn to reduce the level of poverty in the country.
As long as the above conditions remain, you're going to have unrest throughout the region. And the level of corruption within the Iraqi government is so high, it's doubtful that any meaningful progress will ever happened. If the US was administrating the country, we would be able to ensure that everyone has a seat at the table, but also be able to start to take care of some of these issues. Of course, at this point security is the highest concern, and as we have seen, the Iraqi Army definitely isn't capable of handling that..