>They wouldn't, it's just deliberate confusion. If an arm of the government knows someone is there illegally they're meant to report them for deportation or other handling, not offer them infrastructure and rights,

You forgot the obvious middle ground, milk them for every penny.

If we had multiple classes of IDs you'd see every damn government transaction that requires ID come with a surcharge or different fee schedule for people using the variant that can be obtained without being a legal immigrant because those people can't complain.