But if their dual citizens that means they're not solely Americans, they're American/Taiwanese or American/Mexican.
It has nothing to do with loyalty, for many of them it boils down to the fact that one parent was an American citizen and the other parent was a citizen from a different country. They are just as much a member of their foreign culture through one parents side of the family as they are members of American culture from our side of the family.
Also passports aren't used to leave a country, they're used to get back INTO a country. Yes you can get a travel visa to visit a foreign nation but if you're already a Citizen of that nation why not have a passport that will automatically allow you entrance. Not to mention you are guaranteed entry with a passport where you can be sent back with a visa.