I was reading online discussions about it and somebody suggested that Krampus was wearing Santa's literal face, implying that Krampus killed and skinned Santa, and that was why he was punishing everyone and not just bad children; there was no one left to keep him in check. Apparently actual Krampus lore contradicts this but I found the idea compelling in the sense of making the story even more terrifying.
I know it would've been cheesy but there was moment in the movie when there's a rumble on the roof, the radio and Christmas lights suddenly turn on momentarily, and I was genuinely hoping to see a Santa ex machina. I guess it was deliberate misdirection.