Actually we have a very pertinent case in point as to why this is not a good idea. In the US, we have long had a system of credit reporting that is based on national Id. The (absurd) presumption was that if you know the national Id of some person and their name, birthdate etc., you must be that person. The problem with this is that finding out the the national Id of someone is becoming increasingly trivial. The result is that people are regularly impersonating others for illicit gains. The problems for the actual owner of that Id can be really big.
This idea that you are proposing would actually contribute even more to this issue but that's not really the point I am making here. Changing your national Id is very difficult in most (all?) countries. Once someone has this information, it's useful for a long period of time and victims of this struggle for decades to deal with all the constant problems such as debt collection agencies calling them at work or terrorizing their families. I recently heard about a woman who's national ID was stolen and used by another woman who was going to prison.
The problems with this kind of system are very much like the use of biometrics. If my fingerprint is my Id and someone can reproduce it, then everything I touch is potentially giving away my identity to a thief. People can even get it off a photo as in the link above. If anything, we need to get away from the use of such unchangeable Ids being used.