I think I'm probably equally as productive as a person that really knows their editor of choice. The productivity benefits mostly just come from knowing what things your editor is capable of.
However, I subjectively feel a twinge of frustration whenever I need to take my hands off the keyboard to reach for a mouse. So using vim makes a massive impact on my day to day wellbeing.
I don't care about the productivity, I do care about not doing tedious things.
There are many syntax-aware vim verbs (ci[ or ci” for example) that save a lot of time and let me get back faster to thinking about the what and not the how. Too much time on the how and my ADD kicks in, sure as someone walking into my office and trying to talk to me.
Keybindings seem to engage your brain in a different way and make the activity more fun, but I don't think it's actually any more productive.