Earlier quoted context omitted.
Out of curiosity is there actually any chipset with the algorithmic ability to add more than 2 numbers altogether in one operation (without having to store intermediate results)? I'd also think looping is far closer than recursion to how we tend to manually calculate things (either entirely in our heads or using a pen & paper or even a basic calculator). (Edit: looks like a number of other posters have made the same…
Chips have ability to run vector operations that can add a bunch of numbers. The issue is that recursion in software development is relatively rarely about arithmetic operation. For example, you might want to traverse a tree of objects (like a filesystem folder) to run some operation on them, etc. In this case the intermediate information is pointers to where you are currently processing various folders in your tree…
And yes I'm very much in agreement that the real power of recursive algorithms is when working with tree-like data structures.