I imagine this is a problem when you're trying to leave the country to go back home, and they're asking you why you're not showing up as having entered the country...
There is a classmate of my daughter (UK) whose family went to vacation in California. On a whim they decided to visit Mexico, but had left their passports at their San Diego hotel. They were allowed into Mexico without a passport and had an, ahem, interesting re-entry to the US. I’m surprised they were actually allowed back after several hours.