I do not see why a longbow (and only a longbow) could not be used by Strength and Dexterity a like. It seems only fair. Str characters should have a decent distance range weapon. Throwing things is not enough(plus they are not as cool). Just like dexterity has its crossover weapon to melee (the Rapier 1D8 finesese weapon). Strength based Charactersneeds one too(the Long Bow 1D8 ranger weapon). Just makes sense and that's how we play in my game. Its not OP the fighters are just happier with thier options.
Bows have a 'pull' that correlates directly to the strength of the archer. A bow with a much heavier pull than you can handle can't be used (or even strung) - a famed mythological example of this was the bow of Ulysses (Odysseus), which only he could string. A heavier pull means more energy imparted to the arrows, so greater range, and presumably, power. Conversely, if you use a lighter-pull bow, your extra strength won't impart much extra force on the arrows. Historically, well-trained archers were quite strong.
In AD&D, ranged attacks used DEX 'reaction/attacking modifier' to attack, and no bonus to damage, but there was an optional rule that you could use specially-made heavier ranged weapons to get the strength bonus to damage. Colloquially, we called 'em "Strength bows." In 3.0, they became a standard rule, IIRC, and were called 'Mighty.' The composite bows had the option of having the mighty quality for a specific strength.
That option is not present in 4e which used the 'heavy thrown' quality to give STR-based characters a ranged option. It was simpler, but it did kinda disadvantage them when it came to range. 5e continues that simplification with 'finesse' melee weapons and 'heavy thrown' ranged weapons giving DEX/STR exceptions based only on the weapon used. Unfortunately, that gives DEX an even greater advantage over STR, since the got-to finesse weapon is essentially equal to the best one-handed STR weapons, while the best heavy-thrown weapons are decidedly inferior to bows. And, it's arguably 'unrealistic,' that archers don't need any strength.
A simple way to get a STR-based archery option is to just create a bow - call it the Composite Bow or Mighty Bow or something - and give it the 'heavy thrown' property, so it can use STR, as well as ammunition and load - and the clear notation that you're not, in fact, throwing it.
Another simple option would just be to have all ranged weapon attacks use DEX for attack, and STR for damage.
For more complexity, give bows in general a pull, rated in STR, the bow gets it's rated STR bonus to damage, but if the wielder doesn't at least match the pull he has disadvantage (if weak enough, couldn't use the bow at all), and if his STR bonus is higher, still only gets the bow's rated damage bonus. The same kind of rule could work for crossbows, a STR minimum to load by hand, no STR min if you use mechanical assistance, but the load time is longer.