Not sure if this has been mentioned but if, God forbid, an employee assaults another when they are sharing a room, the company will be sued for this policy. Does the company have general counsel/in-house lawyers?
Well exactly and back to an example I gave, sure it's probably mostly ok if two same sex straight people share. But what if someone decides to bring someone else back to the room? What if one person is gay and ...there's so many ways this goes wrong. Construction is a pretty conservative field. If some guy finds out his roommate isn't straight or already knows that and is very uncomfortable with that, it's just a whole mess that very easily bleeds over into other aspects of the work. Do you require people to disclose sexuality so you can assign roommates appropriately?!
That's why I think if you go to HR and point out the liability facet they'll want to shut it down.