Dueling swords in a small part of the world for a relatively short time period. Your general statement prior was that thrusting is superior. I agree but within historical context. Take the rapier to India. Maybe it flourishes and becomes the de facto dueling weapon but maybe it doesn't.
The samurai carried katana because there was no outside forces that made them change their weapon needs-- i.e. cultural isolation. Had rapiers made an appearance there we likely would have seen a different dueling scenario.
My point is that unarmored dueling needs are specific and inherent to the era in history and the geographic area in which they occur. In Japan for example the battlefield arts were largely abandoned during the Tokugawa Shogunate. The Shogunate united Japan from its warring state era (constant civil war) and brought an era of peace relative to the constant fighting that had occurred previous. Budo changed from dealing with armored battlefield opponents to unarmored single combat duels. Why then if thrusting is supposedly so superior is there no rapier-like sword during this period? The answer is for the Japanese there was no need.
Also rapiers (with a very few exceptions) make awful cutting swords. There are a few examples of rapiers with flattened sharpened tips but the vast majority of rapiers lacked proper blade design and bevel to be an effective cutter. In fact rapier were often not sharp at all until the very tip and could be grabbed by the bare hand-- this was the case with many medieval swords. The dull blade of a cut and thrust sword (dull except the final section of the blade) could be gripped to allow for a powerful strike with the pommel of the sword to an armored opponent. Basically the sword could be flipped around and used as a mace.
By the way, in the rapier vs. katana argument all things equal I give 67% of the matches as a draw or to the rapier. Katana were specialized and being shorter cutting swords were at a disadvantage to a rapier. Katana can certainly win the duel it would be a difficult task though. I have no illusions of a katan (or any other sword, including rapier) being inherently superior or perfect.
The Japanese actually had a weapon that gave them an edge over a rapier-- the o-dachi. I can poke you from far away!
This last part is obviously a joke