Maybe the disconnect, then, is that you don't consider programming to take place in the real world. I don't share that experience, any more than someone coding batch jobs on punch cards or an author committing chapters via typewriter. Maybe the medium has parts that only have meaning within our minds, but we are real (dammit!) and we punch out those characters with our real hands and we get frustrated and deal with impedance mismatches and want to scream and laugh and cry. There is a piece of us that lives in what we build. It's evidence that we are real.
This ties in with your second point. There are uncountably many ways to accomplish the goal of making a chair or writing a program. And if you are a carpenter working on a one-off matched dining set for a fickle client, the problem might not be as clear as even many software tasks are. Your skill and experience is highly likely to play into the eventual form and structure of the finished work. The customer might not know where you hid the dovetail joints or dominoes, but they can absolutely notice the grain continuity and lack of obvious engineered joinery evident in a factory piece.
If you don't care, then fine! You can focus on the other things that bring you joy. But I hope you can appreciate that some of us want to experience solving these problems with a bicycle for the mind instead of a Waymo.
