> I am failing to see how the inherent probabilistic nature of the technology can be fully overcome.

This is common in image generation pipelines because if you find an image you really like, you can store the seed and then reproduce it with small tweaks, otherwise - to quote Borges - “Look at it well. You will never see it again" User-facing deterministic pipelines do exist for generative AI.

I know you make this argument in your post, but that's really the answer if you want repeatable results. For a classifier or a detector, determinism is a requirement, but for an LLM non-determinism desirable property because it feels like a more natural conversation. The downside is it's extremely difficult to replicate a response without pointing the model to an earlier conversation.

And specifically for the RPG case, don't you want non-determinism? You don't want the model spinning up the same identical person if you say "Generate me an NPC character sheet for an innkeeper". This was a complaint that people had in the past, that models would regurgitate the same scenarios or the same jokes.

Where I suspect DMs run into trouble is not randomness, but lack of self-consistency in worldbuilding. Say you generate an NPC and then refer back to them later and the model gets some details wrong. You could compare to a system like Dwarf Fortress where everything down to the genealogy and faction relationships are rigidly generated.