Why better fighters would not solve the Vietnam War

What changes if US Air Force F-4s are replaced one for one by F-15Cs and F-16Cs, while Marine Corps F-4s are replaced by F-14s and Hornets?

The United States would dominate the air war more completely, but the conflict's logistical, political, and public-support problems would remain.

The date of the aircraft substitution is unspecified, so the reply considers a Vietnam War setting. Later fighters would provide a large technical advantage, but winning the air war would leave other problems unresolved. The exchange contrasts winning the population's support with interrupting enemy logistics, then adds the need to retain support at home. Reporting body counts as if they were a score repeatedly reminded Americans of US losses. The comparison with the Battle of Britain turns on the difference between a distant war and an existential threat that much of the population could see overhead.