> Which elements of 'top leadership' believed this?
Macnamara. LBJ. Kennedy.
> For whom would that 'show' be for?
For the American people, for Congress, for the world. To prove that the US stands by its allies and can still win wars. To prevent accusations of being losers by domestic political opponents, both in the same and different parties. Pretty basic stuff, these political dynamics are in play in nearly every war.
> This directly contradicts your first statement. Did US leadership think they were winning or not?
You are misreading the line. I am saying there were not winning either in reality nor in the leaderships minds. The US leadership did NOT think they were winning.
> Imagine how history would have changed were, in 1965, the Pentagon were able to fight on it's own terms?
How do you propose to fix the problem of Chinese troops overwhelming any serious success like they did in Korea? That's nearly the entire reason the US couldn't fully commit to destroying North Vietnam.
How do you even fix the problem of having unreliable and problematic allies in Southern Vietnam that could never really rally the country properly?
You have learned no lessons.