These cool names come about because they are supposed to hide the meaning of the mission. The military now uses two random and meaningless words picked by computer to create secret names for missions or plans (for example, the operation to build the pre-production F-117 stealth aircraft had the mission name "Senior Trend"). I'm sure there is such a name for the current operation, but it is kept internal to the Pentagon. The public names ("Operation Iraqi Freedom", "Operation Desert Fox") are made by public relation wings of the military or administration.
You may not realize it, but the first and second paragraphs here conflict, and it is the second one that is right. Light skinned vehicles have a purpose (liason, light transport, personel transportation), but they have to be used for convoy duty because the military was never planed or designed to do wide scale peacekeeping and police action and there are simply far too few real convoy vehicles. The fact that there are no Army vehicles between the Humvee and the M-2 APC (except for the few Clinton-pushed and very-hated-in-the-military Striker wheeled vehicles) is a sign of the cause. The military branches (except for the Marines, somewhat) have all centered on getting big budget contracts for sexy weapon systems at the expense of usible equipment for police and pacification for lots of reasons, including winning the intra-service competition for money and because it impresses Congress, who hold the purse strings. The last thing a military wants is to fully equip itself for peacekeeping actions - first because such purchaces are non-sexy and individual (which limits how the contract can be split for pork purposes) but most of all because it means the military will actually be used for peacekeeping.
Peacekeeping? Was that even considered by Bushco? I believe they thought when Dumbya landed on the aircraft carrier the war was over. Why else would Rummy only want 50K troops originally to seal the deal in Iraq. They seriously thought Iraqis would be kissing our feet and picking up arms to police their own country in no time flat. IIRC they thought most of this expedition would be wrapped up by election time. My God the bungling of this war will be a case study for military strategists for decades on how NOT to plan & execute an effective "nation building" operation.
Yet you we see such vehicles used for a variety of purposes in any western armies. It's not about cost as the fact that commanders in the field feel a need to make an impact in any way possible. The thing is that troops always come up with way to remedy their problems. The question about budget allocations is a problem that crosses party lines. If you were to put a budget for the military that didn't include pork barrell spending, it would get tossed out before it gets to a vote. Screwing any military by those who don't serve in uniform, regardless of political leaning, is SOP in most countries. Because the countries that would be called up to do "peacekeeping" didn't want in because they feared that they would actually be forced to do their jobs their soldiers trained them to do.