Tony Vargas
Legend
There really isn't one, and I think that's something 5e has gotten 'right.' Remember the convolutions past editions did trying to make light/DEX fighter concepts work, at all? How many Duelists and Swashbucklers (and demands for same) have we seen over the decades? Now, in 5e, you want to play D'Artagnan, you just put a high score in DEX and pick up a rapier.It also speaks to a larger problem with Finesse... what exactly is the trade-off?
Sure, DEX is das uberstat, again, as a result. But the margin isn't huge, and the DM can always tweak and tune balance w/in his party if there's a STR guy that's languishing. Or, of course, remove or tweak stats of finesse weapons.
Going back to the 3.5 finesse feat style rule that DEX can add to hit, but not melee damage, would be a more extreme mechanical 'fix' if you really wanted to disfavor the option (rather than remove it entirely) to get back a more medieval feel.
Oh, you could also restore the medieval feel by replacing the Rapier with the more period-appropriate, if obscure to modern readers, Estoc or Tuck.