Re: ID Card
A National Insurance number is an identifier for an individual, but you can't actually prove that it is you - it doesn't have a photograph or name associated with it at a level that most departments can access.
A Passport or driving licence will prove your identity, but the document ID generally isn't linked to any other system so doesn't link you with your various government records outside of their specific responsibilities.
The reason for an ID card is to effectively supplement all the disparate other IDs you may possess and permit you to reference any service you are associated with without having to carry all your cards/documents. It should not supplant them - at least initially - you should be able to present any or all of them.
For example, European ID cards are accepted travel documents in the wider European area, but are not valid for global destinations like Africa or Asia where they need a passport.
The key point about the Estonian system is it enables universal proof of identity and storage of records while providing transparent proof of access and lack of tampering. THAT is unique in the European sphere today.