There’s actually nothing in the rules that says a ranged weapon can’t have the Finesse property, and in fact, darts have it. The precise wording of the effects of the Finesse property is: “When making an attack with a finesse weapon, you use your choice of your strength or dexterity modifier for the attack and damage rolls. You must use the same modifier for both rolls.”
So, darts can be used with the wielder’s choice of Strength or Dexterity, and I am suggesting that to give bows a leg up over crossbows, you give them this property as well.
Perhaps phrasing it as “going the 3e route” obfuscated my meaning. My intent was to suggest that, if simply giving shotbows and longbows Finesse seems like it would make them too powerful, you could consider leaving them unchanged and adding “composite shortbow” and “composite longbow” to the weapons table, which you could leave identical to their non-composite counterparts, but with the addition of the Finesse property.