Rig, even a legal US resident might be afraid to call the police to report a crime - against themselves or others - if they didn't have access to their birth certificate or a passport and maybe didn't have a driver license, so that they feared they would be hauled off to the police station and detained until such documents could be provided.   
Suppose a "Hispanic-looking" woman was out jogging, without taking her "papers" with her.
(Who routinely carries a driver license, etc., when going for a walk or a jog?) And suppose she is raped or otherwise attacked while away from her home sans papers.   Is she supposed to wait till she can get back to the house and look for proof of legal residency BEFORE reporting the attack?   Such a delay could well make it harder for the attacker to be apprehended, plus, she might have been injured in the attack.

Or how about this fairly common scenario:   Your purse or wallet is snatched while you are away from home.   Now you have no ID on you, so if you contact the police and they "have reason to think you might be in the country illegally," instead of focusing on solving the crime and catching the thief, the police are required to look into the legal status of your being in the US.
And when your ID is stolen, are you not supposed to go anywhere until you can get a replacement?