Cascaded vs. non-cascaded bridge-tied load circuits using opamps
Nice, (+1 for opa454, I didn't know this opamp.)  I've also used BTL to get more voltage out of low voltage high current opamps.  (OPA569 driving a TEC.)  As far as your question.  I guess the traditional approach doesn't have any gain balancing.  (It's just a unity gain inverter.)  And I've never been worried about noise in the driver stage.  So my only answer is simplicity.