If you want a national estimate that grossly undercounts, just multiply by the 20 field offices. Now we’re in the hundreds of thousands.
If the paperwork is that easy to duplicate, it's on the government to make it more difficult, not beating in the faces of citizens until they produce documentation they don't have.
Hundreds of thousands of aliens with fraudulent documents seems like a huge problem to me.
Keep in mind it’s US law for every alien to keep documentation of legal status on their person at all times (US code 8 USC § 1304(e)).
Since we know fraudulent documents are not uncommon, then immigration officials must have some powers to validate a person’s status if uncertainty remains.
Obviously in case (1) you can just detain and carefully identify people, since they're actually doing dangerous things and you'll have probable cause to detain them. Note that this was the case that nearly all the 2024 election rhetoric was focused on (i.e., deporting the "rapists and murders".)
In practice we're seeing that the true goal is (2), rapid emergency deportation and arrest of non-criminal immigrants. There is absolutely no emergency that requires this to be done quickly or carelessly, such that there's any risk to US citizens' (or immigrants) civil rights. It can be done carefully, with strong evidence, without violating civil rights. But of course, violating civil rights and creating disorder appears to be the goal.
