Some eventing riders use an overgirth, an extra strap that fits over the saddle and girth, as a precaution against the girth failure during the cross-country phase. On a running martingale, one of the rings could slide forward and catch on the hook stud connection on the rein end. Prevent this hazard by fitting the reins with rein stops of leather or rubber. The ring can't slide any farther forward than the stop. Before you place any article of tack on your horse, evaluate its value and its dangers.
Tack holds in heat, and it has a potential to rub.
If you don't need it, don't put it on the horse.