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.
I'm not sure of your position. Are you saying that in today's battlefield, with enemies that we're most likely to face, Corps level personnel are as likely to be captured as those in units closer to the front? No.
Maybe killed if we face an enemy like China,… maybe. But any force that could do that's much more likely to actually honor the Geneva Convention prisoner of war rules and not gang rape our women. We don't fight civilized nations. (Now you're thinking of WWII) We're at real risk of fighting barbaric POSs like Iraq, Iran, Syria or NK, and they won't likely be capturing people at the Cops HQ level.