I’m a Vim user, but I don’t agree with that argument about cognitive load. When typing in a normal editor, you just type letters and those same letters typed just show up on a screen (as in Vim’s insert mode). The mouse is pretty intuitive too in a normal editor: you have a device that controls a cursor on your screen and clicking performs an action.
With Vim, I don’t think the commands are quite as intuitive (this might be a skill issue of mine), but I do think I am faster without a mouse because of fewer movements required (having to grab my mouse, move it to where I want, click and then move it back to the keyboard vs. just typing a few letters).