Um, no. The US was actually extremely soft in Vietnam.

Um, no. The US actually dropped "one million tons of ordnance" on North Vietnam (where US air strikes killed "approximately 52,000 civilians") and "some four million tons of bombs" on South Vietnam ("the most bombed country in the history of aerial warfare—a dubious distinction for an ally"). The US actually supplemented those bombs by dropping about 70 million litres of herbicides on Vietnam, including over 40 million litres of Agent Orange and Agent Orange II, such that "millions of Vietnamese were likely to have been sprayed upon directly" and over 2 million hectares of Vietnam were sprayed repeatedly. (This excludes the anti-personnel gases and tens of thousands of tons of napalm the US employed during the 1960s alone.) And a working group in the US Department of Defense actually reckoned it could substantiate hundreds of reports of US war crimes.

The execution in the "infamous Vietnam execution photo" wasn't even being carried out by a US person; it was not the sort of thing I had in mind. I was thinking more of, e.g., the My Lai massacre.

Is that what you consider "extremely soft"?

The idea that the US had been "tactically winning" the Vietnam war is, so far as I can tell, far from universally held. Can you explain to me why I should believe your description rather than anyone else's?

While it is true that the threat of the Japanese Empire was successfully ended, it inevitably spawned a dozen other problems in other scenarios.

By these standards, pretty much everything one does of any consequence in international relations spawns a dozen other problems.

As soon as you use "sufficient brutality" and prove yourself to be dangerous, you will prompt everyone else to become more dangerous.

Everyone else is quite capable and willing to become more dangerous without any prompting from us. Becoming dangerous is useful for its own sake, not just as a response to others being dangerous.

While it is true that the threat of the Japanese Empire was successfully ended, it inevitably spawned a dozen other problems in other scenarios. Most notably, it paved the way for the Cold War.

In the sense that Communism and the Free World wound up crashing once the common enemy was removed, yes. Your argument about nuclear weapons seems to boil down to arguing that if the US hadn't developed them, no one else would have. I'll let you clarify in case it's something not quite this silly.

let's say the U.S. gets fed up with the situation and drops nukes on strategic Iraqi and Syrian cities.

You don't have to go that far. How about having the government not treat rumors that an interrogator may have flushed a Koran down the toilet as a moral crisis.

Next thing you know, Iran will panic and get its own nukes,

Um, Iran is already developing nukes as fast as it can, despite the US not being very brutal.