In this particular case, it's because Americans have somewhat unusual deep-seated distrust of our own government, which has lead to pretty well-organized opposition to any federally mandated form of identification. Officially, the only two real semi-universal lists of American citizens available to the federal government are A) Social Security numbers (which aren't ID, they're just a unique identifier, and aren't legally mandated, just incentivized), and B) The Selective Service Registry, which IS legally mandated, but only for fighting age men. (Fun fact: this is why American men still need to register for the draft, despite the US not having a draft since Vietnam. This registration does not suggest that the US is any closer to re-instating the draft than any other country that eliminated their draft, as it would still take an act of congress, just as most countries can reinstate their draft with an act of parliament. The reason we have to register is that officially, the federal government otherwise has no idea who is even eligible to be drafted).