Oh it does. Rapiers do have pretty heavy pommels which makes them terrible for swinging (because centre of balance is almost on the crossguard/basket) but are very mobile. The reason why they're bad for swinging isn't because the blade itself isn't heavy, but because most weight is lower down on the blade, meaning that the weight at the tip doesn't actually work the same. In comparison, a weapon without a pommel and a heavier blade, with overall weight similar as rapier, would have better swinging abilities but would be generally cumbersome (compare a falchion and an arming sword. Weights are similar, but swinging a falchion about is slow as hell, although yes, it has very powerful cuts).
However, every sword's pommel is needed as a form of counterbalance. What you really want is to have the point of balance is around... say, 6-7 centimetres away from the crossguard on an average arming sword (although that term in itself is kind of mixed). Anything further, and trying to hold the blade becomes a bother. Anything closer and your cut doesn't pack enough punch and you have a glorified stabbing weapon.
Specialist weapons are different, of course. I mentioned a falchion, which is basically a cleaver. That thing's point of balance is around half way through the blade, even though it's also controlled by the pommel.
Also, just as a side note for imagination. Imagine a sword, and its point of axis being on the crossguard, and it moves up and down. Now, as you move the point of balance further away, the sword falls faster, delivering a greater blow. However it also becomes harder to control and stop.
