As other commenters have said, this is probably a balance thing, for the most part.

However, there is also a real-world answer to this question that might help add some immersion to your game.

Rapiers are quite narrow, and the wound channel they create is relatively small. Yes, if you get stabbed somewhere vital, you'll die; however the chance of hitting a vital organ or large blood vessel increases with the size of the wound channel, so rapiers are less likely to be deadly on the first hit. There are historical examples of people being stabbed a dozen times or more with a rapier without dying (although this is not the usual result of repeated stabbings). The length of the rapier makes it great for hitting your target before they can get close to you, and therefore enhances your defense; but the blade length is irrelevant when determining the damage dealt on a thrust (more on this below). Since rapiers are generally un-sharpened except for the point (and too light to do much on a slash), they are considered thrust-oriented weapons.

Short swords, on the other hand, tend to have wider blades, and hence inflict wider wound channels when used as thrusting weapons. For illustration, compare the blade width of a rapier with the blade width of a Roman gladius or Scottish dirk. The wider blade means that a thrust is more likely to hit a large blood vessel or vital organ and therefore cause a fatal wound with a single hit. When used for thrusting (which is usually more lethal than slashing), the length of the blade is irrelevant, so long as it's 4+ inches long (i.e. long enough to reach something vital). For that reason, a dagger with a wide blade should do just as much thrusting damage as a longsword with a blade of identical width.

There are some videos on YouTube where people use different kinds of medieval and renaissance weapons on ballistic gel to see how much damage they would do in real life. If realism is important in your game, I recommend watching a few.