Yes, the United States should take over Iraq and make it a state, because that is the only way that we are going to have lasting peace in the region. Iraq is one of the more moderate countries, and there are a lot of people in the country who want the American way of life. They would fit right in.
We've already seen this happen before. The US had set up embassies in Iraq, but were quickly overrun by Iraqis. Thus the uprise of Isis. Also, taking over a country is very old fashioned. The last time something like that happened like that was the Gulf war (pretty recent actually). What would be actually beneficial is that Iraq would have a stable government through the help of the UN. More diplomatic and political discussions of peace, stability, and sustainability regarding the country.
A mother way would be to let the Middle East be. The US was developed through lots of life loss and bloodshed, as we humans never have the same opinion, but we eventually became a very stable and 1st world country. This is a heartless idea, but this is how peaceful( Ish ) nations came to existence.
We have already attempted to make Iraq a peaceful nation and as soon as we started to withdraw troop, ISIS immediately began to take over. I think it would be impossible for us to force them to become a democratic state until they are ready to do that for themselves. We also don't need to lose any more American lives in the Middle East.
The US should absolutely not take over Iraq - This would almost certainly lead to massive conflict and large losses of life. While we may feel morally obliged to interfere with international affairs, this has historically led to lengthy conflicts with no real resolution to the issues at hand. Trying to take a country over (especially one so geographically distant from the US) would be a logistical nightmare, would likely never be accepted by the population, and would never be worth the investment of resources to do so.
I think there is no way Iraq should become a State. I feel that is a complete mess over there and will continue to be and don't think it needs to become part of the United States. I think it would be a disgrce and make the United States look even worse and I want no affiliation with Iraq.