Thanks for the impressions.
This would help if the amp was actually being turned up to the max. If the attenuator or whatever isn't at 100% though, then there isn't any need for more gain. I've had a look at the numbers, and with a 1.4 Vrms source playing material at -20dB, an 8x gain B22 (not balanced) will take the HE6 to 97.5 dB (103.5 dB for 8x balanced). Enough for most I expect. And that's only pushing 20mA, not even close to the standby current let alone the max.
We're not going to be able to solve this one online, as I haven't heard the amps you're talking about (excuse the noob). I would just encourage more blind testing, because if there's really a reason the B22/B24 don't sound as good as some speaker amps, then (AFAIK) nobody in the world of electronics knows why. It certainly doesn't show up in the measurements, as the B22 is pretty much perfect. I'll leave that one to sound science , best to not derail the thread any more, cheers all.