The trouble with that is if you flip the feedback switch while the amp is on, you'll get large pops and bangs and you are likely to do damage to speakers or headphones.
Also, we're not fond on having any type of feedback to depend on switch reliability. If there would be any deposit on contacts after a while, things may go drifting, making noises, even channel imbalance...We prefer normally soldered traces and component leads with anything feedback related.
Now, even if this is not a real issue, that we're just too cautious, there is a problem of open loop vs. closed loop amplifier gain.
With feedback on, and if it's 20dB, the amp will loose 20dB of gain, so we would need another voltage gain stage stage to get the gain back...
With feedback off, you have too much gain, the volume pot never above 9 o'clock, and there is one stage too many in the circuit.
I mean, all of that can be made to work correctly, but it just didn't seem to be a nice, simple and pure concept, with that unnecessary extra stage in the circuit, when we're focusing on ribbon headphones.
As for conventional headphones, it doesn't work right, simply because of the noise. This is actually a kind of a "loudspeaker" power output, designed to pump out 7+ Amps of current into the headphones. Because it's a normal power amp, it doesn't have low enough noise floor for highly senstitive transducer that you stick close to your ear.
It would literally be like connecting a speaker that has 130dB/W to a speaker tube amp, so the hum and buzz would be ever-present and very annoying.
Granted, feedback would reduce that to a very low level, but then the point is lost. You're listening to ribbon headphones without feedback, but have to use it for all other headphones. It wouldn't be the same sound at all.
So, it comes down to horses for courses, and this is a one trick pony...but no other pony can do that trick and that's just the trick we need