Many of the accepted models of contemporary theoretical analysis have absolutely nothing to do with music written at present. Case in point: 12-tone analysis. I cringe when I talk to students that spend the only 4 months of their undergraduate education dedicated to contemporary music theory doing find-the-row exercises for some prof that thinks it's still 1965.
I confess that I have my students identify rows, though certainly not in all pieces and I usually don't spend time identifying every single form of the row in a given piece. Much like with Roman Numeral analysis, I regard find-the-row exercises as an opportunity for the students to find landmarks in unfamiliar territory. Just as a rapidly modulating development of a Beethoven sonata can seem incomprehensible until the modulations are worked out, a serial piece by Schoenberg can seem to be randomized noise to students who have not spent any time listening to atonal music. Finding the rows, showing how the composer used a system to organize the notes in a decidedly un-random way, allows the students to listen with more open ears and more confidence in the compositional control of the author. Thus we can get to larger picture ideas about form, emotional content, and the like.
In addition, cool relationships can be found, such as the tonal implications and relationship to "Es ist genug" of the row in Berg's Violin Concerto or the canonic text painting of Dallapiccola's Goethe-Lieder. These are not always readily recognizable phenomena, but that doesn't always matter.