"how else would a naturalized citizen have arrived in the US in the first place, except with a passport in their name?" -- part of the complexity of the case, as I note, is that he did in fact enter illegally, smuggled across the border. He did not have to enter illegally; he could have simply presented his passport at any border crossing (or, lacking a passport, an affadavit), but nonetheless he did.
The second case was minor children. Known by ICE and immigration judges to be citizens. Deported deliberately to accompany their mother. This was in conflict with the mother's expressed wish for them to remain with other relatives. At no point were the children charged with any sort of immigration crime, fake or otherwise.
I agree that American citizens are not required to carry proof of citizenship and agree that they should not be required to present papers to prove citizenship.
But you are describing a world that does not exist. No US citizens are being deported mistakenly (Garcia being the lone exception). Notably, this has not always been the case -- under previous administrations there have been numerous cases of citizens being deported, but in the Trump administrations this has not been the case (with the exception of Garcia). We are not living in a nightmarish dystopia.