Perhaps when LLMs introduce a lot more primitives for modifying behvavior such a programming language would be necessary.

As such for anyone working with LLMs, they know most of the work happens before and after the LLM call, like doing REST calls, saving to database, etc. Conventional programming languages work well for that purpose.

Personally, I like JSON when the data is not too huge. Its easy to read (since it is hierarchical like most declarative formats) and parse.

One pain point such a PL could address is encoding tribal knowledge about optimal prompting strategies for various LLMs, which changes with each new model release.