Fine-tuning works very well for style (as opposed to factual knowledge), which is all we're trying to achieve here -- as another commenter put it, it's a "comedy bit" for a company Slack.
In fact, fine-tuning for style works well enough that we find it pretty easy to just re-train when new models come out. There's sometimes some YAML-fiddling required to get training frameworks to work with different model series (e.g. a DeepSeek series model vs a LLaMA series model), but it's not too onerous. IMO, the ideal ML pipeline looks less like the bespoke process common these days and more like a materialized view (shouts to pgML). That's easy to automate and so reduces the gap with prompting.
On the other hand, it seemed harder to craft a generic system prompt and a generic retrieval system that would work across organizations to define user communication style.