As I said in a different comment, we US folks have decided as a society that we don’t want to have mandatory difficult-to-forge national ID. When asked this question democratically, US voters and their representatives have repeatedly* turned down this option and explicitly banned the Federal government from issuing Federal ID cards outside of optional passports for international travel. We made this decision precisely because we distrust the sort of Federal government that would require us to carry that sort of document. There is nothing accidental about this, and you can find explicit statements of this bipartisan consensus all over real Federal legislation; there’s really no possibility that we did this by accident or without due consideration of the tradeoffs.

You’re correct that this lack of standardized documentation makes the immigration enforcer’s job harder, since they can’t just force people to produce proof-of-citizenship on demand and they can’t detain US citizens, and they can’t necessarily trust every paper document they’re given. I’m sympathetic! But that’s the tradeoff we’ve made as a society. The answer is not “throw out the rule book and risk depriving citizens of their rights because our job is hard.” The answer is: respect the rules you were given and due the best job you can without depriving US citizens of their rights.

And PS this situation is hardly unique: we also make ordinary cops’ jobs harder by requiring them to respect suspects’ civil rights and demanding probable cause to make an arrest. It’s tough! The result there is that cops have to work harder and be smarter; they don’t just get to detain anyone they want just because they might vaguely hypothetically be a criminal.