Well, that particular conversation typically happens in relation to something like a business rules engine, or sometimes one of those drag and drop visual programming languages which everyone always touts as letting you get rid of programmers (but in reality just limits you to a really hard to work with programming language), but there is a lot of overlap with the current LLM based hype.

If we ever do get an actual AI, then yes, AI will probably end up writing most of the programs, although it's possible programmers will still exist in some capacity maybe for the purpose of creating flow charts or something to hand to the AIs. But we're a long way off from a true AI, so everyone acting like it's going to happen any day now is as laughable as everyone promising cold fusion was going to happen any day now back in the 70s. Ironically I think we are more likely to see a workable cold fusion before we see true AI, some of the hot fusion experiments happening lately are very promising.