It's a rather ...unconventional suggestion, that clearly was not thought out. There is a high risk someone doing that ends up stateless, i.e., with no documentation or paperwork establishing citizenship in any country. The US may arrest such a person at the border - and then imprison them - and then try to deport them back to their country of origin. But what is your country of origin? It may mean a stay in immigration detention indefinitely. There's no guarantee authorities would believe a claim of US citizenship at that point. Citizens who've gotten in that position (usually cases of mistaken identity and/or misbehaviour by US customs) have been deported, and they don't always make it home. It is a potentially Kafkaesque nightmare and I would not advise intentionally putting yourself in that situation.