Actually, while we're on this topic, for those who don't understand why current is needed:
Noting this, how does volume correlate to properly driving a headphone in this case? As in, what does the headphone sound like if it can't produce enough current to create the isodynamic field?
Volume is related to power. Power is then related to current through the equation P=I²R.
Simply put, you would require a high enough current to drive the headphones at the volumes you need.
If the current is insufficient, the volumes you require cannot be achieved anyways.
Also, no current is necessary to create the isodynamic field.
It is produced by the permanent magnets in the headphone.