Well, are you sure? What is fidelity? Of course, you are saying it is an exact replication, what goes in, comes out, but if the ear is more comfortable with the natural harmonic progression as opposed to an unnatural harmonic envelope, why is "nature" not a good thing?
Hit a wood block, there are harmonics, overtones that occur naturally. Extra harmonics following the same pattern would sound more "real" than a lack of or different harmonic presentation. Same can be demonstrated with the human voice IMO.