I've spent some time thinking about this earlier as this indeed is one way a teacher would introduce a young child to programming (but by using actual bread, pb and j). An important underlying question is why kids would learn programming in the first place if they're not going to be programmers... one answer, which applies to math as well, is that it is learning another way to think. The whole point is that it is difficult to specify exact behavior, especially when you can't lean on someone's already established understanding of the world.
Another related idea (if I don't misremember) is brought forth in the book "Program or be Programmed": that it's not the programming itself but learning that things powered by software are intentionally (by meticulous instruction, like above) made to work like they do rather than just happen to work a specific way. Which hopefully leads to the realization that we have agency and can change how things work in the world, should we want to.
Now, some people are arguing for teaching kids programming via vibe coding and one the one hand I can see their point but on the other hand, it was never about the programming in the first place. Vibe coding is kind of the opposite of the two ideas if you don't first teach them. It's making the PBJ-making teacher/robot go "oh, so you want a PBJ, here's one". There's no learning new ways of thinking. It's also making it seem like things are not intentionally made to work a specific way but more just happened to become that way. Some of that empowerment and agency is lost, I feel, although I can see that there is agency in creating things too.