I strongly agree that programmers should learn touch typing at some early stage of their career. We do a lot of typing - code, documentation, bug reports, StackOverflow questions, community interactions, emails, dev.to comments... - and you are correct that time is too valuable to hunt-and-peck that all in the long run.
Personally, I learned touch typing in middle school (yay for "Mavis Beacon Teaches Typing"!), and I currently type at between 85-105 WPM, with 90+% accuracy. That skill has helped me tremendously in every aspect of my career.
While I'm at it, can I also say programmers MUST learn good spelling and grammar! It says a lot about a coder when "ebverythng they type looks like ths lol hey evrybdy see what i mean rotfl". The impression that poor/lazy spelling and grammar gives is that the coder does not care, is poorly educated, and/or is therefore probably incapable of following the even stricter syntactical rules of programming. Coders should take the time to use proper spelling, capitalization, punctuation, and the rest of grammar (minor exceptions granted for live chat.)
For me, the effort involved in proper writing is minimal, purely on merit of practice. Learn it alongside typing, and practice it diligently. Over time, it'll become second nature.
On that front, if the rules of grammar escape you, I strongly recommend the "Writer's Digest Grammar Desk Reference" by Gary Lutz et al.. Similarly, if you want to improve your writing style, "The Elements of Style" by William Strunk and E.B. White is an excellent reference.
Programming is ultimately about communication, so the better one can communicate the better a programmer they will be.
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