Well yeah, you're right. It's not that the character changes it's just that my perception of it does.
It works with any archetype. Once you slap moe, yandere, tsundere, childhood friend, etc, it makes the character SEEM 2-dimensional* even if they're not.
*figuratively speaking of course...
As an example - Misa from Macross, Faye from Cowboy Bebop, or Isako from Dennou Coil. All well-written characters but when I think of them as tsundere it sort of ruins it.