You would not expect the CEO of a large multi-national company to manage all of the details of every department within their company. When you combine all 5 of the armed forces together, it's far more complex than any company on earth, and managing the military is not the President's only responsibility.
The President's direction of the military is also bound, to some degree, by the Legislative and Judicial branches of the government. For example, they can't declare war on a country unilaterally. But those restrictions, while important, are not particularly constraintaining at a day-to-day level. The President has wide latitude to direct the military as they see fit. That includings projecting military power as deterrents against hostile foreign powers or engaging in short-term, small-scale offensive operations abroad.
So, no, Presidents aren't going to the front lines and directing troops like kings of old. That went out of fashion around the time of Napoleon. But good business leaders don't micromanage their workers and departmental details, either. They realize, hopefully, that doing so would do more harm than good.
The peak of the Southern government was '71-72, prior to the Easter Offensive by the North. The Tet Offensive had destroyed the Viet Cong in the South (needed to be entirely back filled by the Northern troops), so at that point the RVN had full control over much of the South. The fighting had died down to the point that work on social programs like land reform, actually install competent provincial leaders, etc had an opportunity to improve the life of the average citizens in the countryside (the major cities saw little violence over the war with the exception of Tet and a few other attacks).
RVN wasn't a democracy by Western standards, but it was a government that could at least provide security, development and work towards building up the country.
When the Eastern Offensive happened, the US was limited to air power (all troops had left by ‘73 but the drawdowns started in ‘69), and the ARVN made a good showing at the battle of An Loc. They were capable of being an effective fighting force but needed US support to counter the USSR and Chinese support the North was getting.
After '72, Congress cut off all aid, Nixon was in no position to force things otherwise (i.e. Watergate) and the writing was on the wall since the South didn't even have enough gasoline for their military vehicles.
The South was a corrupt government with plenty of nepotism and stealing of US funds, but if you visit Vietnam today you’d realize not much has changed on that end.
Imagine if instead of being red-baited into escalating the conflict in Vietnam, LBJ had directed the money to his Great Society programs. Generational poverty would have been drastically reduced, more people would be educated, there would be less crime, and we would have more and better science. There would be less government suspicion, enabling the federal government to attract more top tier talent, leading to a more effective government. That's the real travesty. Even if South Vietnam got a supported non-communist government, it wouldn't have gotten the financial and technological support that South Korea got from Japan, so chasil's vision would not have happened.
And LBJ did offer a Great Society funding scheme to the North and it was rejected as “trickery”.
There is a great book on LBJ’s decision to escalate - I can’t remember the title, but it’s 300 pages long and only covers a few months in ‘65 when the decision to escalate was made.
People like to think the decision was made in a vacuum but it was influenced by everything going on at the time and geopolitical risk going forward.
LBJ made a decision (there were members of the inner circle who wanted to pull out) based on what he knew at the time. It turned out to be the wrong one.
The documentary covers various phases of McNamara's career, including his contribution to the Tokyo firebombing raids in WWII, and a short bit about his work at Ford Motor Company between the wars, but the Vietnam war part was the biggest section.
And right about now we are witnessing another. Against an opponent with nukes.