Culturally anyone can understand why the Japanese practice these arts for reasons of heritage and tradition. But of what value are they to Westerners? Especially given that the likelyhood of being armed with a sword when needed is extremely remote.
First, the sword as well as all weapon arts completment the unarmed martial artists. They more effectively impart sometimes vague concepts such as "maai" (combative distancing) and "kime" (focus) much more effectively than unarmed martial arts ever could.
Second, when training with any implement the body is conditioned by it. By making the weapon part of the body, the body advances itself to compensate for the weapon. Learning how to extend your energy through an innanimate object raises your capacity to deliver empty handed strikes.
Third, unlike any unarmed arts, weapons arts especially the sword develop aggressiveness. And not in the negative conotation. In Kendo you constantly seek to kill your opponent. Immediate action combined with actual closing and hard contact with the opponent trains the mind and body for combat much more effectively than tthe tag and dodge of unarmed sparring.
The actual styles (Ryu) and schools (Ryu Ha) are much less important thatn the way they are practiced. Today, especially in the west, sword arts are practiced in two forms, traditional and sport kendo. Sport Kendo is fine for an aerobic workout but offers little more than that. It is unrealistic in the way it is practiced. It would be like using football as a means of defense, it can be done but better ways exist.