VIM is not only about typing. It's about editing, which involves making a small change in one place, then navigating somewhere else, and making another different small change etc. This is where VIM is unbeatable, because of ridiculously many fast ways to navigate and edit intelligently (in a very small amount of keystrokes). You don't have to type 120 WPM do be faster in VIM, but if you are a fast touch typist, you can get insanely fast in VIM.
Besides once you can edit faster, it's surprising how your "speed of thinking" also improves dramatically :D.
Agreed. Navigation through a file without using the mouse or arrow keys greatly speeds up misc. edits in a large tree of files.
Other upsides are the ability to delete text without the backspace or delete key, and to perform more complicated operations on a file, such as full regex search-and-replace, macros, and so on.
Really what it boils down to is a powerful text editor that lets you keep your hands on the keyboard at all times- which of course is not appropriate for all tasks, but very useful for many.
This is a huge deal, and you've done a great job expressing it. I definitely find that I think faster as a result of being a vim user / being in vim. Since most of the actual editing gets thrown to muscle memory, all I have to do is think 'gosh it'd be nice if that refactoring happened' and it does, while I'm on to thinking through the next step.
I'm constantly mortified at how rarely my co-workers/employees use vim macros. I make vim do the hard parts for me.
Besides once you can edit faster, it's surprising how your "speed of thinking" also improves dramatically :D.