Personally, I find that when I start thinking "hmm, I wonder if I could write a program to automate this" is when I quit the pursuit. After figuring out the basic tricks to sudoku, it turned into busywork. (Or trying to micromanage StarCraft)
(Tagentially, if you want to automate programming, then I'm going to find myself a different field, because I have no interest in the results of sudoku puzzles. I especially have no interest in managing agents, which I see as junior-dev bullshitters, and would not enjoy managing such a team in real life)
(I absolutely relate to your experience with sudoku etc. Of course, writing a basic sudoku solver is also interesting.)
The thing is, software architecture and systems design can also get the hobby treatment. I've found that I'm happy to have a short discussion with ChatGPT and have it barf out a few hundred lines of a concept, then refactor and maintain it myself. Or come up with a few different pieces that can be written fairly easily, let the machine skip over most of that tedium, make sure they conform to the interfaces I had in mind, and then verify for myself that the system actually comes together the way I imagined.
Of course, it does help a lot that I can understand the code, and work with it line by line if necessary. But SICP teaches us that it's abstraction and composition all the way down. So I feel like I'm exercising the same skills while not letting myself get intimidated by the sheer amount of initial typing or the self-doubt (instinctive immediate review of the code, you know) that creeps in when I try.
I think if that were always true, calculators would be banned in schools.
Surely the "point" might be different things to different people depending on their exact situation/context.