> There's a huge difference between being able to write "programs" (for example the ones described here are ~5 lines) and being able to write a large and very complex piece of software, which such an AI would undoubtedly be.

That's true. real-life programs that programmers get paid to write are typically more complex than 5 lines. Any AI good enough to replace real programmers is going to be very close to good enough to rewrite itself.