I mostly work in Python, which has a repl (though I'm sure not as complete) and sometimes I poke around in it. But if I am working on a real project, or even just a small script, I always want to run it from the beginning on every invocation, because anything short of that is not proof that it works.
"Editing a running system" sounds like a nightmare! How could you ever know things would actually work?!
This is why Clojure developers love immutable data and pure functions so much. Say I am writing a web frontend for managing a list of users, and I want to implement some kind of filter and grouping flow on them for some business reason. Since I know the users are immutable, I know that when I am evaluating code in the browser to test out exactly what filter logic is correct I am not actually changing anything about the system.
In the case of the REPL you are playing your program. You can play a file, a function, or half of a function. Until it sounds right.
I lack the skill to use music notation for composition, so I rely on my instrument to give me feedback. And I lack the skill to execute the program in my head before I press compile, that's why I rely on the REPL.
> How could you ever know things would actually work?!
Eventually you would run the project from beginning to end to make sure it works. REPL just allows you to by-pass that during development for rapid feedback. If the project takes 2-3 seconds to boot, we are talking about a difference of getting feedback in milliseconds vs several seconds - which makes a huge qualitative difference in developer workflow.
The point is precisely that you do NOT have to run it from beginning on every invocation. Doing it once in a while is enough.
I had similar preconceptions from Python's REPL. Now after reading (at the least the first section of) the article and watching the video my mind is blown.
I've also been dabbling with Emacs Lisp recently and it appears that you can do basically the same thing.