Could you give some explanation as to why you believe/how you have seen that cutting swords are more numerous and well known than thrusting swords? The truth of the matter is, is that most swords are capable of fulfilling both roles. While you may think of a sabre as an exclusive cutting weapon, you can actually thrust with it by aligning the point with the angle at which you thrust into your opponent. On the other hand, you may think of a rapier as being a thrust-only weapon, but historical fighting manuals often show cuts being thrown with rapiers to the head, arms or legs.

Very few swords can only perform one function. A katana might not be as optimal for thrusting as a longsword is, due to the shape of it's blade, but you can still thrust with it. Likewise, a rapier might not be as optimal for cutting as a sabre, but you can still cut with both.