It's just a WHOLE lot easier to manage and update the settings.
If you're using Notepad to do your development and putting the code out on the server, I would agree that there is little benefit, but if you're using Visual Studio and you build your website and publish it, you're publishing the pre-compiled dlls and not just updating text source code (.cs or .vb files) on the server. So when it comes time to update a setting at that point, anything in the web.config can be updated by simply modifying the text file, where as with other changes, you have to re-compile t whole web site and publish it.
And from experience, that becomes tricky when taking over after other developers that weren't careful about ensuring everything needed to make a web site work is in source control. I'm now stuck with a web site where we can't update huge chunks of it because of (kindly putting it) non-standard practices in the past.
Being able to update something without re-publishing the site is a huge blessing in my situation, and you never know who the poor maintenance programmer will be that takes over on your code.
Be nice to him or her. Make it easy to make simple changes.