Our documents detail the outbreak of trouble in a US-UK military relationship which has continued to deteriorate since, with many in the Pentagon feeling "let down" by the "weak" British. But ultimately, history may have shown that the Americans were more right than we were. By 2006-7, Britain's softly-softly tactics had left Basra in near-anarchy - while in Baghdad the US "surge" had brought about a significant reduction in violence.
Nevermind that
The so-called "Dutch" approach (which is largely copied from the Canadians but let the Americans not hear that) has shown to be relatively effective (but not faultless) at least in more low-populated areas. I've no idea whether it has been applied in more densely populated, urbanised areas or, if it has, how effective it has been.
Am I misunderstanding you? Because it seems to me that the European goals were the realistic and legitimate.
To be a little more specific: even if the idiot American neocons had stood back and gave full control of the occupation to European allies (including command over US occupation troops), I don't see how they could have achieved more than relative peace on the surface until a pull-out a year or two later. After which all hell would have broken loose -- and if they stayed longer, all hell would have broken loose anyway. For,