I see this argument come up all the time to argue against typing faster, learning a decent editor, and now typing vs writing. Like with you, the hardest part of my job, and also the most time-consuming, is thinking out the right solution. I draw different lessons from that than you do, though.

First, since thinking is the hardest part, it's important to eliminate as many distractions as possible. Having to break concentration because I'm writing/typing is very unhelpful. Writing or typing with poor typing skills breaks concentration for longer periods of time.

Second, a nontrivial part of "thinking" is actually reading code spread across multiple files. Since I use vim, typing speed helps me to quickly get to the sections of code that I need to review. This greatly speeds up the thinking process.

Of course, I definitely do write stuff out at times, and I find I can think very well with a whiteboard. These are mostly for things that need to be diagrammed out in two dimensions (which a lot of things do need to be).