Die Hard Questions

The problem is that it could literally be any holiday where the office is closed. New Years, 4th of July, insert any holiday and the plot still works just fine. Bad Santa does not. He was already a mall Santa when he threatened to sue because of the black dwarf accomplice, who he most likely met because he was a Santa.

Christmas isn't necessary for Die Hard to happen, it is necessary for the other movies to happen. That's the difference.
The building had to be empty, but still have the Nakatomi people in to open the vault and act as hostages. Leaving the rest of the building occupied introduces too many variables. NY and 4th of July office parties aren’t common. It had to be Christmas.