Well I am a former Violectric v281 owner (balanced in, balanced out) and I know the next model down - v220 is balanced in, single ended out. Pretty sure it was a wa234 owner that told me despite the 3 pin xlr outputs on the front, it was actually single ended signal - just balanced plugs. Correct me if I'm wrong.
TBH, I've never bothered to take notice/ keep records of such things, but if I cared to look, I'm sure I'd find a bunch more among the plethora of headphone amps available today.
As you said, balanced input circuitry sorts out the signal from the noise. Which is separate to the amp section. Once the noise is removed from the signal, it can be amplified with one amp per channel. It may not be as common because people buying gear with balanced inputs are probably going to believe that it should be balanced all the way through, but it doesn't have to be the case.