Ummmm..... when I galloped, I galloped in a cross. When you have a tough pulling horse, a full cross really comes in handy. Good luck to anyone that can ride a direct rein on a tough pulling horse. BTW, exercise riders better know how to "throw" a cross (especially) if they are going to be working horses. So yes, exercise riders DO throw and ride in crosses.
I take it you just went straight to riding races? Never was an exercise rider?