For the analogy to hold, wouldn’t each holder of a Deutschmark also need to be given a (portion of a) Euro? That wouldn’t be easy to do with physical currency,

For the analogy to hold, wouldn’t each holder of a Deutschmark also need to be given a (portion of a) Euro? That wouldn’t be easy to do with physical currency, since there’s no easy way to mark each Deutschmark currency as having been awarded.