Originally Posted by San Rensho
Why reversed on the cross bike, or on all the bikes?
On the cross bike, it works to your advantage because you commonly dismount on the left side. Your right hand is (should be) resting on the top tube before you dismount. If you're coming up to a barrier too fast, having the rear brake lever on the left side allows you to slow your speed without risking a front wheel skid, which could cause you to lose control.
-- A quick side-note: One argument against switching the brakes is that if your right hand is resting on the top tube, then you are pinching the rear brake cable, and you won't be able to operate the rear brake anyway. However, the plastic straw-shaped housing over the exposed portion of the cable (which you should add if you make this modification) allows the cable to slide underneath the weight of your hand. --
As for all the bikes, well, it's very confusing (at least for me) to remember which hand operates which brake unless they're all the same.