I don't think that I'd agree. Do you know how rare it would be to take prisoner from a US Division or Corps HQ Btn? I don't, but it must be very small.
You're thinking of good old-fashioned mass army slugfests from 1943, not the irregular battlefied of 2003. This wouldn't have happened in 1943.
Corps and Division HQs would be prime targets--take one of them down, and you pretty much reduce its formation to a loose collection of brigades without long-haul comms, theater and national intel access, et cetera.