Carrying a crop all depends on the horse you are riding. Some horses never need a crop and others need it once in a blue moon. Top riders tend to know their mounts pretty well, so they know if they need to carry a crop with a particular horse. There is not an expectation to carry one what so ever. Also, every horse is an individual. You'd be surprised to learn how many of those top horses are not as nutty as they seem.
Strength is not defined by physical ability. It is determined by your actions and the compassion of your soul.