If the horses all run the same speed, does that mean that every single horse will finish at the same time? No, it does not. Even if the track was straight, rather than circular (which I'm assuming is what you mean) there could still be competition as horse jockeys could steer their horses to ram the opponents to make them hit a fence and so on...
It's actually not a bad idea, although I'm afraid that it may require a large amount of work for Badspot.