You can't expect rational behavior from governments. In a time of crisis, there will always be some idiot in power, who doesn't want to face reality, or cares about their pet issue more then overall well-being, or feels that they have no alternative options.
Churchill rather typically stated it most succinctly: When presented in late 1941 with the report of Hitlers declaration of War on the U.S he said (paraphrasing a bit from memory on the literature) "So then we do win this war after all.."
As for Japan, SOME of the top people in the government and military knew they were committing slow suicide with their attack (Yamamoto for example, thought it was complete idiocy to fight the U.S) but there were enough fanatical believers to push through their idea that if they could just get the upper hand on the U.S in a preemptive naval/air war in 1942, they might secure peace for their Asian conquests.
Note that the incident is started by North Korea downing a civilian jet, even if by mistake, South Korea reacting, NK going berserk with nukes, US responding with conventional weapons... Hmmm, a bit kind towards the West. The US certainly come out as the level headed guys, which doesn't sound very coherent with recent rhetoric and events.
Saddam Hussein thought that telling the United States to go pound sand was the correct move. He thought that all the talk by the warhawks in the Bush administration was just bluster.
As it turns out, that talk was not bluster, telling the US to sod off was not the correct move, he got to dance the hemp fandango, and 16 years later, Iraq is still in the middle of a civil war.
These kinds of geopolitical failures happen when one country's leadership mispredicts how another country will react to its actions. This can happen in any year, be it 1939, 1941, 2002, or 2019.
They either start by one side believing the other side fired a nuke. (See: Every close call having to do with a communication failure/false detection.)
Or by one side believing that firing a tactical nuke is the only way to accomplish their goal. The battle doctrines of both the United States, and Russia, permit the use of tactical nuclear weapons in conventional military engagements. I wouldn't be surprised if, in a shooting war, some idiot were to actually use a tactical nuclear weapon, believing that it would not escalate into an exchange of strategic nuclear weapons.
It doesn't have to be anybody's decision. Cascading mistakes and system failures happen.
This assertion has no historical basis. Plenty of people stand to profit from such a war. Just look at World War II. Countries, companies, and individuals profited greatly. Even in the worst case of total nuclear annihilation, someone who was prepared for such an event could profit, depending on your definition of profit. In any case, what matters is whether the people involved believe they can profit; however they define profit.