Spoilers
Working out the agent's shorthand follows a particular order is one of the central puzzles. Having the numbers in a random order would detract massively. Being able to instantly infer who was the most recent death is useful to advancement in a lot of scenes.
Also, the agent created the number 1-12 system *before* the agent himself worked out Katherine was relevant. You can see that here:
"[@] Edit: looking back at all the deaths, it's clear there's one that doesn't quite fit the pattern. It took me a while to track it down, but I've now added one more scene that should complete the chain of events."
Katherine can't fit into the same numbering system the agent used because the agent only realised Katherine was relevant much later and her scene was gathered much later.