This is an interesting discussion. I'm deep into a project now (as the sole developer) where I was surprised to learn that the frontend js is about 30% bigger than the backend (python).
In ipython I use autoreload (thanks to a tip on HN) so that the code in the objects in memory is kept in sync with my editor. My workflow is: load up a bunch of objects I'm working on, try to get the expected output, fail, change code in my editor again, check the the output, repeat. Within ipython you can even '%ed obj.broken_function' to edit it directly in vim. There's no doubt that the auto reload discovery improved my efficiency. Aside from the time it saves, I'm able to think of my running code and on disk code as the same thing. Don't underestimate how powerful that is.
But as I said, my code is now mostly frontend code. After over 15 years in web development the reload cycle has become second nature to me. It's silly though. I have a lot of state to maintain in the js and every reload is expensive. In my specific case I could be looking at 2 minutes to even load the objects from the web server.
I'm going to have a look at the chrome options to see what's available in terms of hot code swapping. I disagree that it's important for all browsers to support it. Even just finding a good solution in the browser I do most development in (chrome, presently) would be a major win.