I agree that it was ethical based on the lesser of 2 evils principle, and without the need to invoke the "saving of American lives" part.
Assume the nuclear option claimed ~700,000 souls, and destroyed the great culture of 2 cities.
In Hiroshima, "300,000: Total death toll to date, including those who have died from radiation-related cancers."
The non-nuclear option would have killed many more, and destroyed much more culture. A single firebombing raid of Tokyo killed 100,000.
The double effect doesn't seem appropriate at all in this context.
However, thinking about it more, the nuclear option served to wake humanity up, increasing the fear of war in most, save the most deranged despots.
I hope the voices of those who survived Hiroshima & Nagasaki never fade.
A quick google search revealed these cold stats:
On a lighter note, I highly recommend the new Mr. Rogers movie, which inspired me to visit this Philosophy Stack Exchange for the first time.
One of my favorite lines:
from the Vietnam War era, when King Friday XIII, described as “one of the few remaining benevolent despots,” establishes a border guard