Lemme guess they have no bank accounts, no car, no place to live. All of which require you to show proof of who you are to obtain. You are correct there has never been a requirement to carry ID if your walking down the street. But if you are driving a car you are REQUIRED to carry a drivers license and show proof of insurance. If you live in america and are stopped while driving and cannot produce a license, insurance paperwork and don't speak english its a good chance you are not here legally.
And if you are walking down the street and are stopped all you are required to do is state your full name and where you live. If you have no ID and you are arrested no problem either, they will fingerprint you and determine your ID at the jail. If your illegal? you need to be DEPORTED.