I'm not going to argue it's wholly rational but there's a strong undercurrent of suspicion of and resistance to federal government power in the US. As a result, distributed messy processes are often seen as a feature rather than bug. I realize that it's probably hard for many Europeans to get their heads around this but it's the way it is--especially outside of coastal urban centers. And I don't even really disagree with this general attitude.

There is nothing that inherently requires this to be national. You could have this system distributed over 50 different databases if you wanted. It would require "transferring" people that move between the systems.

That said -if you are afraid of federal/national systems (which is an entirely valid if not entirely rational position) then why have a federal tax authority, national passports etc? It seems like getting the worst of both worlds if you have to run authorities that obviously need to keep track of every living soul in the country whether they like it or not - but then not giving them the tools to do so.

The EU is federal in much the same way (independent states, we don't want the central EU government to meddle too much in state business etc) but then we made sure that the EU government doesn't have anything to do with individuals in the member states, they deal only with the member states themselves. I pay taxes to the EU only indirectly through my home country's tax - so there is no need for an EU tax authority to know who I am, and so on.

The analogous situation for the US would be there was no federal taxes collected from individuals, if states issued passports etc.

My guess is the fear is of national anything, not just ID. Regardless if it's good or bad, state level authority is a big deal to a lot of people in the US, especially those on the conservative side of the fence.