I agree with the OP and @Claritas - a good, realistic bass response is what gives weight and timbral accuracy to a lot of instruments.
I think this whole "classical music requires air" claptrap comes from those who listen to baroque/chamber music or other small ensembles - cos an orchestra at full thunder has enveloping, reverbing bass and warm highs: quite the opposite of the "clear treble, rolled off highs" ideal that so many people seem to ascribe to headphones that are good for classical.
Most rock and EDM rarely goes past 50-60Hz. Organs are one of the few instruments that plumb the bottoms of the last octaves - the sound of bassoons, double bassoons and even cellos gains timbral accuracy with proper* bass, not that polite, rolled off cr*p that is touted as the reference by people who listen to classical music on Harbeth or Spendor or other monitor bookshelves.
*By proper bass, I do not mean "tight" bass. I have no idea what tight bass is cos I have never heard it live. Organs dont sound tight and controlled - they fill the room, they shake your innards, they STAY in the room reminding you of their presence. That is not the same as an exaggerated bass response, though - the impact is in the time dimension, not the amplitude dimension. And this is sort of where all headphones, due to their very nature, get let down. Because they do not have the benefit of room acoustics, they are unable to provide that last bit of timbral accuracy (when using the live sound as reference, as opposed to accuracy of reproduction).
Still, the LCD2s are about as good as it gets here - the Oppo PM1s come close, but are a little on the polite side and lack the same dynamic impact; the HD650s also come close but lack a little something in the transient response compared to the LCD2s. I have the HD800s. I enjoy them with several types of music. Orchestral music is not one of them, however.
However, to put this in context, I am unabashedly in the "my fi", not "hi fi" camp. I know what live music sounds like, and I gravitate to systems that reproduce that more realistically to my ears. That means warm, somewhat attenuated treble, a modest bump in the higher bass/lower midrange (in headphones) and deep bass.