I'm an 18 year old American physics undergraduate student (rising sophomore). I came here after reading HPMOR and because I think that being Rational will improve my ability as a scientist (and now I've realized, though I guessed it after reading Surely You're Joking, Mr. Feynman, that I need to get better at not guessing the teacher's password I know a bit of pure mathematics but little of cognitive sciences (take this category as you will. If you think something might be in this category, then I likely don't know much more about it than core Sequences + layperson's knowledge).
Also, please yell at me if I make claims about history and give no sources. (one of my friends growing up was a huge history buff, so I have a bunch of half remembered historical facts in my head (mostly WWII and Roman era) that I tend to assume are not only true but undisputed and common knowledge). Even in informal settings I should link to, at the least, Wikipedia. (This also ensures that I am not making false claims)
but is it really that hard a lesson to process?
I am going to assume that by now you've read enough of the Sequences to recognize your possible hindsight bias, in your post.
In any case, merely saying that "words are labels" is akin to the guessing the teacher's password; people have said it for ages (e.g., "a rose by any other name" from Romeo and Juliet), yet most people (in my opinion) do not truly understand it.
Being currently subject to a system of ridiculous and often inaccurate course prerequisites, I think that the correct model is to list what concepts (depending on the school and department, listing texts that students are expected to be familiar with or courses they are expected to have taken may be appropriate) students are expected to know before taking the course in question - they can choose to ignore the prerequisites if they so desire.
The only reason I see for "hard" prerequisites (it is mandatory to take course A before course B) is safety courses (I don't know if this is ubiquitous, but at my university, there is a safety course that permits access to the student shop and (I think) is a prerequisite for all courses that require use of the machine shop - this is far more efficient than, say, every course that requires it taking time to give students safety training (as this would grow redundant for students taking large numbers of these courses)