Seems a bit denialist. The VC effectively ended after Tet (which was a military blunder, but a propaganda triumph), but the PAVN took up the fight in their stead.
If you never have the initiative, defensive or offensive, it's hard for the war to go your way. You're essentially letting the enemy dictate the terms of most engagements.
The Vietnamese didn't "lose all the battles". Aside for effectively winning the most important battle, i.e. the battle for Vietnam, they also didn't lose many of the battles they picked. The US wanted pitched battles where its army fared better, but with few exceptions they were denied them. Was it unfair? I don't think so: there's no fairness in war, and it's stupid to meet the enemy where he is strongest, and wise to meet him where he's at his worst. Which is what the Vietnamese did.
Body count? Sure, Vietnam lost there. No surprise, the US was essentially out to kill as many Vietnamese as they could -- the only metric they could muster -- and there's no denying they were good at killing them. Unfortunately, short of killing them all and leaving not one single soul in Vietnam, that wasn't the way to win.
I don't think it was possible for the US to win; they were just one grain of sand in Vietnam's long struggle against foreign invaders.
The "won all the battles but lost the war" narrative is a mistaken claim by the US, which can mostly be explained by the lost face and the painful and almost unprecedented defeat they suffered.
> Initially. At the end, the US airspace was essentially unobstructed.
No such thing as "US airspace" in Vietnam, but I get what you tried to say. It doesn't matter if after years of war the USAF gained dominance over Vietnam's skies: the popular narrative ignores how well the Vietnamese did in the air war against the US, that they had fighter aces and scored many kills. A remarkable feat against the world's largest military power.