Ah I understand now, and obviously having references to other databases is just as bad. I mean theoretically these databases could all be linked without an ID card, but it would be harder and not so transparent.
Much, much harder.
Half the reason for the "ID card enrolment interview" was to get you to bring in your driving licence, passport, NI card, etc, etc, so that all these numbers could be reliably recorded on your NIR record.
If they just tried to go through the existsing NHS records, Tax records, DVLA records etc and link the records together blind, without the subject's "cooperation", I doubt they'd get much better than 90% accuracy. That may sound pretty good, but having 4-5 million individuals linked to the wrong database records would negate all the promises they made themselves about the "benefits" of the scheme to government departments.
Make no mistake, the NIR and enrolment interviews are an integral part of the scheme.
Edits: Edited for spelling.