To be clear, it isn't that a national identity database doesn't exist, they just can't force you to have a national identity
token (that is a power divested to the States). Several legislative attempts have been made to link that database to some other token that is
de facto mandatory even if they don't control it, like (currently) State ID. The challenge is, then, that they can't deprive citizens of rights for not having a token over which the Federal government has no control. The States have not been cooperative in this regard across the political spectrum, albeit for different reasons. So at the national level we either have optional ID tokens, like passports, or mandatory IDs that are not tokens, like SSN.
There isn't one court case that informs the boundaries of the Federal government and ID, and how the government may facilitate the linking of an existing identity token to their database, it is diffused across many. The policy and regulatory practice in the Federal government threads a convoluted path through this precedent, with myriad loopholes and workarounds, and exploiting gray areas that have not been adjudicated. I've worked in this environment, which is the only reason I know about it. Every time they create a database on US citizens, they must articulate the title authority that both allows that database to exist and to be used (use and existence are, somewhat dubiously, deemed separate authorities which notionally allows them to collect data if they don't look at it -- this reasoning is not well-tested).
In practice, the US government outsources identity stuff to companies like Lexis-Nexis, which rely on duck-typing to determine identity since this doesn't require the person being identified to carry a token. Just about everyone carries an ensemble of tokens that are sufficient for identity purposes if you have fewer database building prohibitions than the US government.