Translation: gosh, I don't have a frickin' clue as to what I'm talking about, so I will demand that the other guy do my work for me.
Pick the top 3 wars that seem most likely in the next 20 years.
Korea, Venezuela or Brazil, and either Iran or Syria.
What's the nature of those "civilizations".
None are particularly known for being polite to captives.
Imagine how we will engage the enemy.
In any such war, if we're deploying a corps headquarters, it means that we're putting boots on the ground as opposed to engaging the enemy solely by means of precision strike.
Second, the enemy can be assumed to have figured out the blindingly obvious: namely, that directly engaging American frontline combat units is a rather messy way of committing suicide. Therefore, the enemy is likely to avoid direct contact as much as possible, and to focus on engaging logistics and combat support elements.
Third, the enemy is unlikely to use uniformed forces, preferring to use irregulars who play at being friendly until they see an opportunity.
Weigh the odds of a elements in those battles regimental size unit verses a cops size units being captured.
A frontline regiment versus a rear headquarters? The HQ is by far a more likely target--fewer real shooters, far more "noncombatant" types.
Son, any one of those dirtball militaries have a better chance of capturing civilian women on our Texas border than in a division HQ during wartime. Go play with your toy solders and don't address me again.