So, my recommendation is that the Iraqi Coup be re-cast as an automatic script, rather than a Decision Event, somewhat like it was in SC2 Assault on Democracy (if memory serves).
Once the Axis player has triggered the geographic conditions by getting units in or near Alexandria or El Alamein, then the Iraqi coup happens automatically, the British occupy Basra and deploy the XIII Indian Corps there.
If it's desirable to leave something up to the Allied player, than maybe a DE could be crafted focusing solely on the decision to impose sanctions on Axis Iraq.
If the Allied player says yes, then cities and settlements in Iraq drop to supply level 1, if no, they stay at normal supply levels. Depending on the situation, the Allied player might wish to leave the Iraqi towns at normal supply levels to facilitate a faster move on Baghdad, but I could imagine situations in which it would be more advantageous to reduce the supply levels (for instance, if the Axis has taken Syria and might be trying able to Operate units into Iraq)
BTW, I also think the script and the sanctions, if they are part of a separate DE, should be free for the Brits, for game-balance purposes.
As it is now DE 106 is really one of those "non-decision Decision Events" that no Allied player will ever say "no" to.
Alternatively, if you want to make DE 106 a bit more of an actual choice, then saying "no" could, apart from the Allies saving the MPPs at least have the additional benefit that the XIII Indian Corps deploys in Egypt, instead of Basra.