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, where similar amount of leverage has to be exerted with just a single hand - particularly if your opponent is not also using a rapier. Athleticism is also extremely useful in the added movement of the rapier-fencing style.
This isn't saying Longswords should also be finesse: although less strength is required, the greater the leverage that you can exert, the faster your sword accelerates into a dangerous blow, adjusts direction mid-swing and the harder it hits, the more chance you have of hitting in D&D style combat.
Hence why I have trouble visualising weapons like the Scottish broadsword as finesse.
You're contrasting two-handed longsword use with one-handed rapier use. Concluding that the longsword requires less strength doesn't seem right to me considering how common one-handed use of the longsword is. You also seem to be saying you don't think the rapier should have finesse either. Is that correct?
The purpose of them when used in a defensive manner is the same as a shield: to intercept blows before they hit you. They are just generally less effective at it.
Less effective than a shield, in D&D terms, is contributing 0 to AC. I believe the assumption is characters are parrying and acting defensively whenever possible, whether that's with their weapon, an armored forearm, or some other object. All such actions are subsumed into the combat matrix, represented by attacks against AC or hit point loss, UNLESS you have an additional class feature like the Battlemaster's parry maneuver.
The advantages are that its more socially acceptable to walk around town with a cape, or a dagger alongside your sword, than carrying a military shield.
So, a roleplaying advantage. Perhaps that offsets the loss of +2 to AC.
The issue with talking about Battlemaster maneuvers is that that is only one subclass of one of the options that the OP was considering. Much of the current discussion is regarding Rogues for example.
To be fair, the OP said nothing about a mechanically effective parrying ability being a part of the player's character concept. Nevertheless the issue was broached, I believe, because there's a feeling that a character should get some mechanical benefit for giving up a free hand. The parry maneuver doesn't require a free hand, but it does use up your reaction and a superiority die. Defensive Duelist is similar in that you use your reaction to add your proficiency to your AC. With Dual Wielder, in contrast, you give up a free hand to get a +1 to AC. This also comes closest to the OP's character concept because it lets you use weapons that aren't light.
Again, what if they're not a Battlemaster?
There are several options if you want a mechanical benefit. Alternatively, as I've already said, you can describe any character as parrying a blow, whether the attack is a hit or a miss. You don't actually need this to be framed by the rules for it to be part of your character concept.
