There has to be articulable individualized suspicion of a specific crime to stop someone and ID them, you can randomly do it to people on the street even if they look brown or something.

>asking for ID

The same supreme court ruling you named stated the reason why they could even demand ID was because there was no expectation it would implicate them in a crime. Demanding immigration papers in an immigration investigation would reasonably be asking someone to incriminate themselves if not having them is an element of that crime (for the same reason, if a minor is stopped for say having booze, generally they are not required to give DOB even if the stop-and-ID statute requires it).

The bit you are interested in googling is "general warrants" as one of the things colonists were quite angry about.