That's what you might expect, but it requires another breakthrough IMO. From what I understand of LLMs, they can't be incrementally improved to add logical reasoning since they're just guessing the next word. It's impressive and fine in many cases, but there are many where it's not enough.
They already have some form of reasoning though. GPT4 can solve novel problems. It's certainly not incredible at it, but the incremental logical reasoning improvements have already begun.
It might be stick on the last 10% garbage, just like self-driving cars. Clearly it is an important change, but for some fields 90% might not be enough.
Personally, I think we will do more and more complicated things instead of just being done with programming.
What is lower bound of the garbage that we reach let's say in 20 years? Is it sufficiently low that you don't need someone to go over the output carefully? And if it fails that it won't destroy any lives?