Because until PIC(Provincial Iraqi Control) had happened the UK still had to appear to be in charge. The conundrum then comes about what happens when the presence of your forces highlights that you are not in charge
Sadly I think you are right on the strategy. In terms of policy I think the policy was twofold:
1) Not to rock the coalition boat
2) Satisfy domestic political pressures (which meant for the most part being seen not to take casualties and to be getting out).
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