What advantages do students who learn how to touch type have? Would a student's overall CS education benefit by having such a skill, and if so why not make it a required prerequisite? 



An editor notes that there are three (at least) different ideas here that may be confused. 


Does the user hunt and peck searching for each key for each use?  
Does the user look at the keyboard/hands rather than elsewhere?
Does the user use (usually) nine fingers to type or three? 


Touch typing itself suggests using nine fingers and typing by "feel" without looking at the hands. But there are different combinations possible. In particular, some three finger typists don't really hunt and peck, having internalized the keyboard. Some may not need to look at their hands at all. 

Note: "Nine" fingers as the left thumb is often not used at all. "Three" fingers as one of the thumbs is often used.
Actually, there are a lot of things that benefit a student in CS, such as a degree in Mathematics or Sociology. Likewise interpersonal skills that help a person work in groups. Others are too numerous to mention. 

However, a true prerequisite is a block, preventing advancement if you don't have the skill, so no, it should not be required. 

Some data points. I was lucky enough to take a course in touch typing (on a typewriter) in about 1960. I was the only boy in the class intended for girls who would likely become secretaries. Not especially enlightened, of course. But touch typing has benefited me most in writing rather than in programming, and any CS professional writes a lot, even if they aren't book authors. But there are technical reports, grant proposals, system documentation, etc. that makes typing skill useful. 

On the other hand, I know a lot of professionals, who are also authors, who still use two or three fingers to type and it doesn't inhibit them. The world would be a poorer place if they were prevented from entering the field for the lack of such a low level skill. 

Also, modern hand held devices don't adapt well to touch typing. On a phone, I usually use just one finger since the keys are too small and my fingers are too big for me to use even two fingers. 

But, students should be encouraged to type effectively, of course. But not as a block to advancement. Students should, of course, also be encouraged to develop good handwriting skills so that they can read their own hand-written notes. But that skill is being lost, unfortunately. 

tl;dr: Prerequisites should be required only for required things, not just helpful things. 



I'll also note that it isn't typing that makes programming hard. Neither is it typing that makes writing hard. 

But if a student's typing skills are so bad that they seem forced to used extremely short and uninformative names for entities, then they need to improve. Readability is required.