"Crossing the rows" is a D/G mystique"

Mystique? Not really. A fourth-apart box has most notes in either direction, which allows plenty of options to play with lots of push-pull, or to play phrases with no change of bellows direction, or a combination of both. How you choose to play depends partly on the style of music, partly on the character of the tune, and partly on technical playing considerations.

I doubt many players, other than beginners, play all on one row unless they have made a deliberate musical choice to do so. Even players of English music, for which push-pull is arguably characteristic, mix and match both techniques. To play properly in D it is essential to cross the row to play the G chord.

No mystique about it.