World war by itself would benefit military industry directly. That's not saying that they wish for WW3 in any means as the destruction (or crippling) of society would be huge and it would take many years to recover.

WW3 does not necessarily mean nukes at all. I personally think - based on how Russian generals used the military funding to enrich themselves - that most of the Russian nukes are not operational. They might have some low-yield "tactical" nukes (something like nuclear grenades). And I seriously doubt that US would use theirs since as soon as you use nukes, everyone will and after that there is no winner anymore.

> There's no profit to be made in total global mayhem.

Unless you calculate you can be the last man standing in a world with drastically reduced pressure on natural resources due to depopulation