I learned to program using BASIC on an Apple II. All of the variables were global, and it wasn't until I got Apple Pascal that I had access to a language that had local variables. I immediately saw the advantage of the discipline of using local variables whenever possible because I had experienced the difficulty of tracking down where in the whole program a global variable might be changed.
It could be argued that local variables are just syntactic sugar over a global memory space, but no one credibly argues today that we should therefore only use global variables. Local variables make it easier to reason about the behavior of a program, and it appears to me that functional programming takes that idea even further.