By calling it 'just a statistical model' you ignore the emergent property of intelligence. It doesn't really matter if the computer understands what it says, as long as humans do. And when it comes to AI, i'd say, as long as it's useful, use it. When i use a hammer i never worried if it's internal atomic structure and quantum spins bother me beating it on something. It is an irrelevant question.
Now as for the writers, i understand them. I also think AI at this moment is really not that good at story telling. Yes, it can spit out information. But there's a reason we pay professional writers to write quality stories, instead of the youngest clerk. But, for programmers, they tend to view it in a different light. Programmers don't care or are not afraid of AI taking over their job. They are just happy with anything they don't have to type, so they can focus on other things, like more features, the overall structure, gluing stuff together, fixing bugs etc. Also, it is quite obvious current AI is really not that good at writing (complex) code (just as writing quality stories). And it does make other kinds of errors. Human errors are often typo's. AI errors are often wrong order, failed assumptions, or not understanding the bigger picture how things interact, let alone screens and user input. Meanwhile, it is a very valuable tool that saves the programmer a lot of time and work, so that he can be more productive. But you still have to be a good programmer to use the tool properly. And long paragraph short, i am not seeing why the situation is significantly different for writers, or any other profession.
AI will only replace you if you suck at you suck at your job. Because someone else that is better at their job will do your job as well, since they can be more productive. Also, last i know the world is still screaming for more programmers and more technical people. Or lawyers. Or artists. Or other professions. Yes, AI may develop to the point where it actually does better (than humans), by more feed back, more real world integration etc. But, we are at least a decade away from that, if it ever comes. My hand is not a hammer or plier, it uses fingers which are not made of metal. Does that make the hammer superior to my fist? Of course not.