The US definitely would have used nukes, especially in Vietnam - I believe that the reason the US President is the one with the nuclear suitcase and who it the end decision maker (probably something more people are nervous about now) is because when Truman learned about the nuke project (I'm not sure he had been aware of them until he became president) and used them he was afraid the military would use even more. Former SecDef Perry does a lot around nuclear nonproliferation and has good free courses, a podcast, and a book https://www.wjperryproject.org/