I personally do not make this a question of balance at all, and apparently the same do all those who unlike me forbid metal armor but allow equivalent armor of non-metal materials. I say that it is in fact pretty much the forced archetype which is wrong.
It might not be wrong in a vacuum, just like if there was a line in the PHB saying "elven wizards will not drink beer" and "halfling rogues will not wear hats". Would you like such game? Maybe ONE campaign like that would be fun, but ALL? And what if it was only your character with a dumb restriction?
It might also not have been wrong in an older edition where also Clerics could only use blunt weapons, Barbarians could not be lawful, Monks instead had to be, and so on with various restrictions to half the character classes.
But it IS wrong to enforce such a cosmetic element of archetype in the context of a game where every other character in the game is given near-total roleplay freedom on things more serious than a fabric, and even mechanical limitations can be overcome with feats or multiclassing, but not this one if the DM chooses to treat it as a hard rule instead of fluff. Even moreso nowadays that they're campaigning against alignments for races being too strict, restricting druid armors by material strides with everything else!