Skilled programmers may continue to be able to work with it, but only while their understanding of what the software is holds out. In my opinion there is no learning to be had with these tools beyond familiarizing someone with the beginner stages of what programming arts can produce. Things like version control, explanation of fundamental data structures, easily understood scripts, etc.
But when the "sloppification" creeps in on large projects (which happened before AI but is much faster these days), the opacity of the codebase increases an order of magnitude faster than it's transparency. Thus far LLMs are not immune to confusion or mistakes, and so it stands to reason, it will not be possible to build ever new complex software with this technology.
Because of that, it's trivial to see that the skills involved are still required, but with much less incentive to learn them. Not only is it far, far easier to take shortcuts with Claude than it is a Commodore 64, it also rewards shortcuts with faster results at the expense of true understanding. This means that the next generation using these tools won't be filtered out by determination and troubleshooting to the same degree as the last. The Commodore 64 produced a generation of programmers; Claude Code will produce a generation of administrative software users.
While I'm being critical, I do want to state that administrative software users are absolutely needed in society. It's just not the same thing as what you and I call programming, the main difference being the expectation of creating or at least the capacity to create something new. That is, not another clone of an existing project, or a new integration of an existing plugin architecture. I'm not saying we won't progress as a society, but it's my belief that LLMs won't "democratize" software - they will drown it.