My sense is that finetuning might still have a role if your use is high-volume and with a narrow/specific goal. For example, we have GPT based summaries of our customer contact calls. It's fairly high volume (a typical bank will handle millions of calls a year).
We're considering finetuning for 2 reasons:
(1) the current system prompt with instructions is getting quite large* and we see more challenges for GPT to stick to the instructions. We could finetune with our historic summaries and a simplified prompt to slightly improve the performance of the summaries / lower token count (performance). The idea would be to then continue improving our system prompt again from that new starting point. Exploration still to be done though.
(2) we might be able to finetune a much smaller model to do what the larger model is currently doing (cost, sustainability)
* The larger instruction prompt is because there are lots of specific needs for the summaries (e.g. how to write the summary, what to exclude (health, etc.), what to include (actions taken), and we e.g. give examples of good vs bad summaries to improve performance.