Not much to add to the discussion but here is a link with some info on resistor networks.
In the search for the thing(s) that makes the design of speaker amps inappropriate for phones, this probably isn't it. I'd still like to find it, though, so I can know what a properly implemented headphone section is, and I can look for one in an amp, integrated or dedicated.
In the meantime, I guess I'll trust my ears. I don't hear a veil when plugged into my old Harman Kardon. My HD580s do have a strong mid bass (this is characteristic of them and well-reported by people with dedicated amps as well), and on some recordings (<25%) it can bleed over into the midrange causing a bit of muddiness (depending on how you define "muddiness" and what you're comparing them to). A 2 db cut at 500 and 1000 hz clears it right up. I think this is probably a much better way to deal with it than a different "happy medium," because I can turn it off when listening to the majority of recordings that don't have the problem.
It ain't rocket science.