one would have to introduce a true balanced phono circuit internally.
While the idea of duplicated, bridged, or fully balanced (whichever term you like) is sexy, the idea that this is the only advantage is really not correct. Professional gear has been using balanced signals long before audiophiles got it into their heads to duplicate circuits.
Having a differential input which is not referenced to ground has a lot of benefits for noise. And while I don't think we need full-sized XLR plugs, there are mini-XLR plugs which would work a treat for this. I've often wondered this myself.