the USA left because their will didnt match the will of the North Vietnamese and the Vietcong, true, you may have nuked them, the reason you didnt was the threat of retaliation from the Soviet Union and China
You may have won every batle but you lost the war...you were an invading force on foreign soil... you cant beat a people who are prepared to die...
True we didn't have the will. Not the military but the politicians.
We wouldn't have had to nuke Vietnam to win. We put restraints on ourselves.
We did not "invade" Vietnam anymore then we invaded Korea. They were invaded by the Communists. We were trying to prevent Communist expansion. That's why it was called the "Cold War". The Soviet Union and the United States could not confront each other directly so we fought proxy wars around the world. They won some we won some.
And you absolute can beat people who are willing to die. You do it by killing them. Remember Japan? And it's never the case that everyone is willing to die. Even the Islamist. The tyrants and those in power just convince their people to die for their cause but they very much want to be alive.