Just because someone is dextrous, it doesn't mean that every weapon they pick up is finesse. Most acrobats would have a pretty good Str in 5e D&D terms as well as Dex.
That would merely exacerbate the problem with Versatile rather than solving it.
Firstly, flavour is a thing. Not everything in the race or classes is that way for pure optimisation through games-mechanics.
Personally, I flat-out removed the Finesse requirement for Sneak Attack.
Regarding Elves getting Longsword proficiency, I can think of several reasons:
1) It is traditional. Rapiers are a rather recent innovation, and most elven adults were training with their racial weapons well before the rapier even existed as a common weapon. Thus they train their children in the longsword as part of their upbringing and so on.
2) Unlike the rapier, it is a military weapon, and elves are trained in traditional weapons so that they can form militia to fight should they need to. Elven professional soldiers do tend to be more graceful than those of other races, but they probably still emphasise Str over Dex since requirements such as carrying their kit, overcoming obstacles, and holding a battle-line against a push are Str-based.
and of course 3) as a meta-example: Elves are proficient in Longsword because they have been able to use longswords since well before 5e-power finesse was a thing.