If we were to reach a stage where humans don't write code any more, would there even be a need to have advances in programming languages? Maybe what we currently have would be good enough.

I don't know what future we're looking at. I work in aerospace, and being around more safety-critical software, I find it hard to fathom just giving up software development to non-deterministic AI tools. But who knows? I still foresee humans being involved, but in what capacity? Planning and testing, but not coding? Why? I've never really seen coding being the bottleneck in aerospace anyway; code is written more slowly here than in many other industries due to protocols, checks and balances. I can see AI-assisted programming being a potentially splendid idea, but I'm not sold on AI replacing humans. Some seem to be determined to get there, though.