Cap'n Kobold
Hero
Its easier to stick with just one stat or the other. Its quite easy to justify Str applying to hit due to the greater accuracy of a higher-poundage bow, so I'd just stick with all of one or all of the other.I don't see a problem as long as Dex is still used for aiming (To Hit) with the bow and Strength is used only for the damage die. This Str Bow would cost more to purchase and would be useful to classes like Barbarians and Fighters who have a decent Dex and a really high Str score.
I don't think that 5e needs the kind of granularity where you have to start working out the average of Str and Dex for modifiers or similar. With bows, I allow Str as a nod to balance and realism, Dex as a nod to films, cartoons etc, and don't bother trying to calculate or keep track of the poundage of every bow the PCs pick up.