I'm no expert typist and I can't speak to the OP's claims that a bump in typing speed translates to a corresponding increase in productivity, but I can attest to the fact that simple time spent practicing will improve your skills in almost anything, typing included. If you included a typing run at the beginning of your day and made sure you were using proper form, I think you might be surprised at how quickly and how drastically your typing speed might improve.
The key is simply sticking with it over the long term. A general rule I find rings true is that people tend to overestimate their improvement over a month, but underestimate improvement over a year.
The trouble for me is, what is actually "proper form"?
People I've asked, including on the MonkeyType discord, don't seem to have very uniform opinions about it. Lots of fast typists have highly idiosyncratic strategies, as we see in this thread, but trying to get faster than ~150wpm (tested, which translates to more like ~100 in regular settings) feels to me to be limited by hand tension.
The key is simply sticking with it over the long term. A general rule I find rings true is that people tend to overestimate their improvement over a month, but underestimate improvement over a year.