Does impedance balancing in the far end make no sense?
It's complicated.  If there's truly just common mode noise on the unbalanced line, then it'll get rejected -- or not -- by the transformer.  A transformer that's actually built in a way that reflects your schematic symbol would probably do pretty good, but there's no general statements that can be made.  Unless the unbalanced line is exceptionally well isolated, however, chances are high that common-mode noise will leak into the signal its carrying, and that'll get in to the signal seen by the differential amplifier.  In particular, if it's grounded at both the near and the far end, the scheme probably won't work well.

Note that a place I worked at did something kinda like this -- it used 75-ohm coax video lines in a noisy environment, with both the center tap and the coax shield going to a differential amp at the receiving end.  But the guys designing the wiring had to take care that the coax shield was isolated from system ground all the way to the receiving board.