The programming skill that a CS major doesn't teach

A thousand times yes.

It's often said that there are several cognitive stages to learning to program:

* Concept of variables

* Iteration

* Recursion

* Parallel / thread programming

However, it's also been said:

    "Debugging is twice as hard as writing the code in the
    first place.  Therefore, if you write the code as cleverly
    as possible, you are, by definition, not smart enough to
    debug it." -- Brian Kernighan

Similarly, if my code requires wrapping my head around all of it before I can start or re-start work on it, there comes a point where I can't work on it any more because it takes too long to get it in my head. One interruption, it all falls out, and I've got nothing done.

Writing in "big-project mode" lets me be productive in small chunks, and projects get finished, rather than stalling.

Learning to write your code in small chunks of time helps develop this skill. Definitely worth doing. Definitely valuable.