If you want to find out what something is supposed to do, you look at the documentation, the name, and the context.
If you are trying to find a bug, then you are correct that the documentation usually won't show it (unless the bug is in the design).
Certainly there are environments where you cannot use a debugger, and you are forced to examine code manually. Even then it is often most useful to follow code flow, rather than what variable is changing.
This benefit of semi-isolating when a variable changes is small compared to the other benifits of local variables (mentioned in the other thread). Indeed in most cases having function local variables is itself a way of isolating when a variable changes, as then you know that the variable can only change within the function it is declared in, and the functions called by it.