Here's a technical response:
The HE400i is 10dB less sensitive than (for example) the Sennheiser HD-650. That means it needs 10 times as much power for the same loudness, and thus 3.15 times as much current. The low impedance means another 3 times as much current compared to the Sennheiser. Total is thus nearly 10 times more current - and OTLs are limited by current demand, not voltage.