I think we're entering a world where programmers as such won't really exist (except perhaps in certain niches). Being able to program (and read code, in particular) will probably remain useful, though diminished in value. What will matter more is your ability to actually create things, using whatever tools are necessary and available, and have them actually be useful. Which, in a way, is the same as it ever was. There's just less indirection involved now.
Isn't there more indirection as long as LLMs use "human" programming languages?
We've been living in that world since the invention of the compiler ("automatic programming"). Few people write machine code any more. If you think of LLMs as a new variety of compiler, a lot of their shortcomings are easier to describe.