And impedance is what keeps Frequancy response controlled and steady, if you have to much power and not enough impedance your going to have a little more mids, treble or bass in your music. So a 600 ohm can has the Impedance to resist that additional anything from the excessive power. Ofc, as you mentioned those extras anytings might only be noticeable at extreme volumes.
Frequency response and driver resonant behaviour can be affected by the interaction of amp output impedance and headphone impedance. The power of the amp doesn't really have anything to do with it.