Exactly! How hard would it be to start a national database that is linked to IRS, DMV, police and banks (to start). You are 100% right, they just don’t want to.
It is for the same reason that the SSA will NOT tell you that illegals (how many and where) are using YOUR number. Computers are wonderful things; they do what you TELL them and ONLY that. The SSA overlooks multiple use of the same number because it fills their coffers. They, begrudgingly keep track of your contributions and keep the records for when you retire (by employer, location, etc.). They aren’t telling anyone SHIT!....it is simple to imagine the same kind of reasoning for not wanting to trace absconded ‘alien visitors’.