The USA famously has both passport books and passport cards. The cards are only supposed to be used at ground and sea entry points. This is because the (from the link above), the "passport book is the only document approved for international air travel."
But some people have multiple passports that can be used internationally. What would happen if a traveler boarded a flight using their 'other' passport (with an ESTA) and when they arrived in the USA, they showed their USA passport card?
Theoretically, they can't be denied entry because it is proof of American citizenship, right? Is this one of those - take you into a back room and whip you with a wet noodle until you agree it's a bad idea, and then let you in? Or is this actually permissible?