I do think drivers should carry a whip. They are useful. More as a stronger steering mechanism, and quick reminder that it's time to go.
Any decent racehorse does not need a whip to know wtf to do. The incompetent gambler thinks if someone isn't slashing a horse, the driver isn't trying. Anyone who has ever been around a horse knows that there are some good horses that are a hair lazy, but most good horses will give you all they have with minimal urging. And the other good horse who need a bit of urging need exactly that - a *bit* of urging. No racehorses are noticeably improved for any length of time by excessive whipping.