A US invasion of North Vietnam would have put American troops on China's border. This was seen as out of the question because it was calculated -- correctly -- as certain to lead to direct military intervention by China, just as happened in Korea. This would put the US in another lengthy and costly Asian war with China that would weaken NATO and undermine our position in Europe. This would in turn create a dangerous military and political opening for the Soviets to force Europe to abandon NATO and align with the USSR in return for a guarantee against military attack and a relatively free hand in domestic matters.
Our original goal in South Vietnam was to brake the progress of Communism in Asia. In the 1950s and 1960s, Thailand, Malaysia, Indonesia, the Philippines, Japan, and several other countries in the region were seen as vulnerable if Communism prevailed in South Vietnam. In the 1960 campaign, Jack Kennedy took up that view and criticized the Eisenhower administration's refusal to commit to a defense of South Vietnam.
Once in office, Kennedy put US advisers and troops into South Vietnam. With our men on the ground in combat and South Vietnam's government disintegrating, we were stuck. We then discovered that as much as Kennedy and Johnson and the country did not want to lose in South Vietnam, we had no clear understanding of how to achieve victory.
Worse, the US Army lacked the institutional knowledge of how to defeat a popular insurgency. As it was, Westmoreland -- beloved of his fellow generals but vain and dense as a rock -- adopted search and destroy tactics that put the US tactically on the offensive and incurring casualties in pursuit of a strategy of attrition.
Westmoreland's approach led to absurdly inflated body counts promoted as a false metric of victory, the expansion of US ground forces in Vietnam to over half a million men, and to a collapse in public support for the war effort once the 1968 Tet offensive demonstrated a lack of clear progress toward a US victory. Fortunately, at that dark moment, Westmoreland was relieved and his replacement -- Creighton Abrams -- embraced classic counter-insurgency doctrines. It worked.
Even with US troops being rapidly withdrawn, Abrams destroyed the Viet Cong and pacified the South Vietnamese countryside. When South Vietnam fell in 1975, it was to a conventional invasion from North Vietnam that was enabled by the cutoff of war funds by a Democratic Congress with a large class of anti-war radicals elected in 1974 due to the Watergate scandal and a weak US economy.
If one is looking for alternative history scenarios, one can imagine a free South Vietnam today if Abrams was in charge of the war early on instead of Westmoreland and there was no Watergate scandal. Yeah, I too love to imagine Iowa class battleships pummeling North Vietnam, followed by a crushing conventional invasion, but that is implausible due to the near certainty of Chinese intervention and a US-China ground war.
People shouldn’t discount the endemic corruption of the South Vietnamese regime. It becomes magnitudes more difficult to win when your key ally, the one who you are shedding blood and treasure to defend and protect on their own soil, have a national leaderships that is so completely unworthy of help.