> However, don't you still need to understand the entire program as ultimately that's what you are trying to build.

Depends on what I'm trying to do. If what I'm trying to handle is local to the code, then possibly not. If the issue is what's going into the function, or what the return value is doing, then I likely do need that wider context.

What pure-functional functions do allow is certainty the only things that can change the behaviour of that function are the inputs to that function.