I think it's more reliable to do it on helicopter. At least they're not rounding them on a land based vehicle, Which is more likely to run them over. The exaggeration of the "wild stampede" is not that accurate, Besides, If one or two horses get a broken leg, That's no reason to kill them. Helicopters are also very useful in the fact that you can use 1-2 of them, Whereas you must have more horse riders/cars, Due to the fact that the loud yet calming noise of the helicopter does not force the horses into a full sprint, But rather the helicopter can stay at a safe distance and slowly move forward, Easing the horses in to a quick-paced yet calm trot.
Wild horses have always been rounded up by cowboys on horseback wince the good old days of the wild west. To do it by helicopter is against the long standing tradition. Horses get severely injured in the mad stampede (sometimes for miles) and have to be shot due to the extent of their injuries. Colts fall behind and get trampled. There is less chance of injury to round them up in other ways.