Josh Jasper
Villager
Actually it takes a greater amount of strength to effectively use a historical Rapier than Longsword. The Longsword blade isn't much longer but the increased moment that two hands upon the long hilt can exert means that it requires much less strength to control than the rapier of basket-hilted broadsword
Y'know, I've actually used all 3 of these weapons (longsword, basket hit broadsword (sometimes called "claymore" confusingly enough, and a rapier) with real live combat weight, so I know about about the strength and atamina needed for fighting with each. Also you're mixing up your terminology. A rapier is not a basket hit broadsword. But that's been pointed out below.
For a somewhat realistic representation of basket hilt vs. rapier (discounting the "catch the blade" trick), check the fight scene at the end of the movie Rob Roy. Reach, speed, and deflection are all in the favor of a rapier in that fight.
Now, I count D&D as cinematic, but still, the idea of using a rapier against someone in armor is silly. Against full plate with gauntlets, you could literally tuck the blade of a rapier between your arm and chest and not get scratched, but you have the same hit chance as a greatsword! Back in 1'st edition AD&D, Gygax actually had a "weapon vs. armor" table in the Player's Handboook!
As for a saber being a finesse weapon, that's debatable, not in the least because "saber" is such a broad term. There's cutlases, military sabers, and "saber" from modern day fencing, which is just a heavier form of foil, which is no where near a weapon.
While you're right about the longsword getting the benefit of two hands, it's still an exhausting thing, and a rapier is much lighter and easier to maintain because of how you attack and defend with it.
There are some great videos on youtube of various weapons being used by people faithfully reenacting how real combat might have gone based on books and recorded techniques. It's quite fascinating, and could spice up a game pretty well if the videos were used to inform how fights were described.
Here's a good one for saber vs longsword in which you can really see why calling the blade in the video a finesse weapon makes sense - parrying from the wrist and cuts involving quick arm extensions backed by legs - are important, as well as limiting body-as-target. The longsword is best for making powerful cuts, but is forced into rapier like counters, which do not have the advantage of being able to make the quick, economical parries a saber is best at.