IMO, a 4-conductor mini plug is a much better idea. And they are half the height, allowing for low profile amps.
A little thought put into it, and you can build an amp with a 4-conductor mini jack that will go unbalanced when a 3-conductor headphone is plugged in. So no need for a 2nd jack.
Visually, it will look the same as other portable amps, and it will be harder to justify an expensive cable that looks like it just has another ring around the plug. So that's probably what it's all about.