Eventually, yes ... which is why the passport - and photo - need renewal every few years.
There are other forms of biometric scanning, involving the eyes, the ONLY organs which remain much the same, in certain respects, throughout life. These are not so readily available, for example iris recognition - but the phenotype is truly unique, to an even greater degree than fingerprints. In times of heightened global and domestic security needs, this is not just a matter of curiosity to anatomists ! Retina recognition is also used, but can be affected by diseases.