I think that amongst many, Dex builds are regarded as better then Strength builds unless you want to use a two-handed weapon.
Ironically, the rapier actually needs a stronger person to utilise effectively than a Longsword.
Rapiers were paired with the main-gauche, but it was rare that they would be used in simultaneous attacks as per D&D's dual-wielding mechanic. The main-gauche was for defence and for when your opponent was too close for you to employ your rapier effectively. Generally you would be trying to keep at rapier-fighting distance, not dagger-range.
I think part of the issue is not the anachronism of them both being around at the same time, its the practicality of trying to use a rapier of said full plate.
Of course all this is rather muddied by the issue that there wasn't really a point at which rapiers just appeared. The longsword was always both a cutting and thrusting weapon, and there was a gradual evolution to accentuate the thrust, with cut-and-thrust swords for civilian use growing longer and thinner to improve their effectiveness against an unarmoured opponent using a similar weapon. The point at which these swords became the D&D rapier isn't definite.
Sort of. The rapier was a civilian weapon. For military use people would still be using what D&D would term a longsword as the backup to their polearm. Rapiers didn't see military use until quite a bit later, after armour was almost fully phased out.
You make good points, though we disagree, I think, on what the DnD rapier is, in the evolution of weapons a modern person might call a rapier. IMO, what D'artagnon uses is a later rapier, closer to a small sword than the sturdier, quite long bladed weapon I've got on my wall. It would take quite a strong person to fight case with the rapier on my wall, while I've used blunted and tipped smaller blades more like the later "Dumas" weapon with very little muscle effort, because the are very light and balanced nearly at the guard.
Anyway, a few other points, in response to you and others:
Main gauche: precisely my issue, is that there is no benefit in 5e to a rapier wielder putting anything in their off hand, other than perhaps a shield, unless feats are in and hey take the dual wielding one. A simple, non thrown, Defensive (AC +1) dagger would be great. If the rapier is supposed to model D'artagnon's weapon, then it should be Light. But, as it is, the short sword models that blade better than the rapier does.
Of course, talk of rapiers always makes me want to switch armor to damage mitigation, with shields, stats, and your weapon providing your defense, but I also detest systems that turn a successful attack into one which does literally nothing.
Also, which sword represents the "Viking sword", ie, the swords shaped like longswords that didn't have a haft long enough to dual wield? In 4e, they clumsily call it a broadsword and make it less accurate, but in 5e it just doesn't exist, outside of reflavoring he rapier or shortsword.
Heck, why not rename it arming sword? That vaguely covers a wide range of relatively light one handed swords.