I think you misread the situation. In the abstract, the elite had no particular reason to want a war. But once the conflict formed up, it was impossible for them to get out of without losing prestige. Why was prestige such a precious commodity? Because they are an elite, and a successful challenge was impossible. Of course they had no desire to govern Vietnam directly, or to occupy it in perpetuity. But above all, they had to defeat the challenger.
The British Empire ran on very similar principles. In point of fact Britain withdrew from its colonial possessions because it was incapable of holding onto them, and could not cope with the many challenges to its order. But in almost every instance - perhaps every instance - withdrawal only took place _after_ the defeat of the nationalist challenge. So the defeat of Chin Peng's Malay insurgency was the condition that allowed the British to hand over power to the Malaysian indigenous government; the defeat of the Mau Mau the condition of the withdrawal from Kenya.
The US elite did not have to hold Vietnam in principle, but it was unwilling to withdraw at gunpoint. That in the end was what happened, which demonstrated that elite fears were fully justified. 1974-5 was an era when Capitalist rule really was challenged internationally, with the revolution in Mozambique, Portual, the fiercest year of fighting in northern Ireland, the PLO threatening Jordan and so on. All of those revolutionary movement took succour from the inability of the US elite to retain control of Vietnam.