To say what I think causes a country to go to war would take a book, and NOT a short one. Causing a war seems depressingly easy. In fact the relative peace we have been living in the past half century is exceedingly unusual.
In this instance, I'm talking about preventing war. A major factor is ensuring that those most responsible for paying for the war in taxes and blood (Lower and middle classes) have the wealth and the power to say no. (Convincing them that NO is the right answer is another thing!)
The wealth of the countries themselves is not necessarily the wealth of the people who live within them. Take a look at the so called "Banana republics."
I don't know exactly what you disagree with in my reasoning or what exactly is ad-hoc but I always love to talk about it.
Now, to address a few of the facts above:
Japan and Germany were both desperately poor following World War I. It was only after significant military expansion that they reached the prosperity you mention above. Japan gained most of their wealth through their expansion during the Showa era and consecutive wars.
Nazi Germany started from the poverty of 1933 with the suspension of civil liberties after the burning of the Reichstag. Their economic success was mostly spurred by efforts to gear up their military. By that point it was too late for any middle class to object and they hardly had the power to avoid being sent to concentration camps.
China makes us all look like pikers when it comes to war. Mao Zedong and the Chinese Nationalist party before him engaged in mass killings to make your blood turn cold. The modern PRC is the result of almost constant wars consolidating the region we now refer to as "China." Before the 20th century, the countries that make up modern China were engaged in almost constant warfare.
As for Mexico, they barely have anyone to go to war with anymore. In fact, part of the reason there is a wall between the US and Mexico in Nogales is because of a war between the two about 100 years ago after World War I.
Mexico seems to mostly be wrapped up in insurrections and criminal organizations lately though. I wouldn't be surprised if some intelligence agency cooked up most of Mexico's problems during the 1960s to keep them weak and it's just been burning since then. Sort of a Cold War toxic waste spill... But that's pure speculation of the quality used in light fiction.