Vim won't speed up your typing. It'll speed up your editing. Adding/discarding/modifying large blocks of text, or spread-out blocks of text. It'll let you think in terms of moving this block there, replacing these words, duplicating these patterns, etc. The efficiency increase comes, in large part, from allowing you to make steps that are closer to how you think.

And even if we're talking about 20% of your time, improving that 2-10x is nothing to shake a stick at. 20% of 10 hours is 2 hours, if Vim makes you edit 2x faster, that's 1h saved, per day. And that's without accounting for other work you could move to your suddenly more efficient plaintext mode, and the work you don't even consider doing because your editing experience is too painful (it sometimes work the other way too; there are things I won't do in Emacs, but I will in IntelliJ, where project-wide, language-aware refactors can be done with two clicks in full confidence that nothing will break).

Typing and thinking are almost the same thing to me. I'm either writing code, or bullet lists with things to do, concerns to take into account, things I've learned, etc. Text file is an extension of my memory, and a place to distill, manipulate, and organize my thoughts.