I have a simple (*mumble* cheap) portable music player that allows file organization through one mechanism: unnested subdirectories listed alphabetically under the root with files listed alphabetically in each. I started pondering the best way to divvy out subdirectories and files to reduce searching time. The number of subdirectories ideally should be small, so it takes less time to select the desired subdirectory. But the number of files within each subdirectory ideally should be small as well, so it takes less time to select the desired file after selecting the subdirectory.
To cut the self-indulgent story short, I ended up reading about B-trees on Wikipedia. However, since this application has a maximum depth of one, a B-tree would be inappropriate. Yet I was sufficiently inspired to come up with my own set of insertion algorithms based on a subdirectory minimum of 5 files and a maximum of 10 files (in passing, note that these parameters meet the B-tree criterion that a full tree/subdirectory can split evenly into two acceptable trees/subdirectories).
Some might say that it's ludicrous to approach this task in this way, given that I "executed" the algorithms by hand inside a file manager in lieu of writing any code and the low-capacity music player contains less than 300 files. Thus, I lost time by analyzing the problem via a theoretical lens and formulating a general solution. I'm practical enough to acknowledge that reality.
My point is that algorithms and data structures are everywhere if one has the right perspective. And this is not strange compared to other specialties. Artists see lines and shapes and visual patterns that I wouldn't notice unless someone told me. Mathematicians see quantitative relationships (or more abstract stuff - as in abstract algebra sometimes drives me nuts). I could list numerous examples like doctors, lawyers, mechanics, architects, psychologists who all see aspects of their surroundings differently than me.
This is the part of vocational training that's hard to teach: to mold one's mind until the subject matter is a familiar mental frame or toolkit. The reason that professional software developers should study the "Computer Science-y stuff" is so that they can recognize and organize their thoughts, thereby avoiding the trap of attempting a solved problem or attacking it in a naive manner. They don't need to memorize what they can find on the Web or in a book, but they need to know enough to comprehend and adapt what they find!