a lot of countries can't really defend their own airspace, so this would just mean that iraq would go back to how a lot of countries are.
the iraq government is in a strange position over this. the idea that it lacks the capability of defending its own skies probably would not go over well with the iraqi populace (assuming they knew about it). but at the same time, the presence of u.s. bases, including airbases, in iraq already isn't popular with the iraqis. so the iraqi government can solve the first problem by inviting american air power to stay, but that would perpetuate the second problem. and a continued american military presence in iraq after the pullout date is more obvious than its air vulnerability. so the iraqi government has an incentive not to issue the invitation and to ignore its open skies as much as possible.
it also occurs to me that the biggest loser if americans ended protecting iraqi airspace would be iran. one of the reasons why israel hasn't bombed iran is that the u.s. won't allow israeli planes to travel over iraq. without such overflight permission, israeli planes wouldn't be able to make it there and back safely. effectively, the u.s. is protecting iran from israel. and oddly enough, that protection started with the bush administration who also refused to allow israel to fly over iraq to strike iran. without an extension of the american presence in iraq, an israeli strike on iran would be a lot more likely after 2011 than it is now.