I have not read's Rota's paper, so I am not sure what point he is trying to make. Though I have glanced at the abstract, which begins with:
It has been observed that whereas painters and musicians are likely to be embarrassed by references to the beauty in their work, mathematicians instead like to engage in discussions of the beauty of mathematics. Professional artists are more likely to stress the technical rather than the aesthetic aspects of their work.
Maybe this statement is explained and supported in the main text, but, at first glance, this difference in attitude does not strike me as obvious (I'm pretty sure I've heard more discussions about technical aspects from mathematicians than from artists).
To come back to your question, the fact that the untrained and the trained experience beauty differently is by no means specific to mathematics: the trained benefit from having a rich context that dramatically alters their appreciation of the aesthetic aspects of a work; I cannot think of a discipline where this would fail to be true.
What does it mean for high school math? Well, just because I've lost some of my enthusiasm for Euclidean geometry since high school, because I've discovered more beautiful things still, it does not mean that the nature of the aesthetic emotions I feel for Euclidean geometry is any different from the emotions I feel for other beautiful mathematics. And if the intensity has somewhat waned in the case of Euclidean geometry (and I'm not even sure it has), it was certainly very powerful back in high school.
So, basically: who cares if the beauty that one shows in high school math class does not meet the standards of beauty of professional mathematicians? What if it makes these folks go "meh"? The teacher is not talking to them, but to the students! So, as long as the students experience the same kind of feeling of mathematical beauty, the work is done: they know there is more to this, that mathematical beauty is out there.
To finish, a couple of tangential remarks:
- I'm not sure I buy the whole premise anyway. To me, some of the most beautiful ideas in math are commonly seen at the high-school level: they are beautiful because they are so simple yet so powerful (coordinates, change of variables,...). Though, on the other hand, I'm not sure it is possible to appreciate the beauty of these ideas without the benefit of hindsight.
- I have purposefully stayed away from the question: What proportion of students can one reach with that?, in part because I have no idea how to answer the question, and also because this discussion would be so system- and country-dependent that MO is not the place for it. But I think this should be part of your introspection.
