Regardless, I don't really think that the examples you give have much to do with the IDE vs (editor+plugins) debate; they're to do with the amenability of one's language to static analysis. Certainly code modification features are available to statically typed languages that aren't available to dynamically-typed ones (and this may explain why users of the latter are less drawn to IDEs), but there are compensatory benefits to using a dynamic language. Let's not get into that one, though, eh? One eternal flame-war per thread is probably sufficient. :-)
And I'm guessing your fancy refactoring tools probably don't correctly handle the case where part of your code is in one language, which then automatically builds code in another language to compile into the main project. I've never seen an IDE that didn't get in my way with that workflow, and that's the secret sauce that my programming style cannot live without.
Yes, they do. IntelliJ products are capable of updating XML bindings for renamed Java classes/methods, reasonably good guesses about JavaScript/Python functions used in maps (i.e. with their names used as string keys, outside of the AST).
I don't want to be judgemental here, but it seems like you yet have to meet the really big codebase.
It's true I've never really worked on a project with more than a million lines of code, though. My core work is more on the scale of 300,000 lines of code.
Another example: you want to abstract a chunk of code into a new method. Easy, select the code, refactor it out and provide a method name. 2 seconds.
You want to reorder the way the arguments appear in the method? 1 second.
You want to know if a variable is in use anywhere? 1 second.
This stuff is painful without an IDE. I don't know what you do in life, but I find this functionality indispensable.