they think there is an acceptable risk as long as the situation is continually reevaluated
Really, what exactly is an acceptable risk in the eyes of the airlines you mentioned?
Here is an up to date assessment from a neutral European country:
xxx citizens are advised against all travel to Iraq because of the extremely dangerous security situation and very high threat of terrorist attacks. xxx citizens currently in Iraq are advised to leave.
The threat of kidnap of foreign nationals across Iraq remains high. Individuals have been kidnapped at their residence, work and in transit. Kidnappers do not discriminate between nationalities or religions. Those kidnapped include individuals who had security arrangements in place and some of those kidnapped have been killed, including two xxx citizens.
Terrorists and anti-government forces have carried out numerous attacks against places frequented by foreigners, such as hotels and restaurants outside the International Zone. Westerners and places frequented by westerners, including hotels and restaurants, have also been attacked inside the International Zone.
There have been attacks on international organisations, including the International Committee of the Red Cross, the UN and non–Government Organisations.
If you consider your presence in Iraq is essential, you should have adequate and continuous professional close security arrangements and ensure they are regularly reviewed.