The proposed rule does two things: makes archers want to stay out of melee to avoid disadvantage (they already do, but it removes one way to avoid it), and substitute Str for Dex static mod to damage. Rogues don't care about the static mod to damage because most of their damage comes from sneak attack; and Rogues can also use Cunning Action to either Dash away from combat or Disengage out of it before shooting. So Rogues (and Fighter/Rogues, Sorlocks, etc.) become relatively more attractive as archers, and yet all of the logic for why ranged combat is attractive still applies: you can maintain mutual support amongst all the party elements while still gaining the defensive advantages of being out of range of the bad guys, and you can also force the enemy into a Hobson's Choice. (E.g. if you have a ranged-heavy party with a Mobile Shadow Monk in it, the enemy can't engage you at range, but he also can't afford to hole up in a cave and wait you out or else the shadow monk will kill him. The countermeasures for one are the sweet spot for the other.)
There's a number of things you could do to try to fix the problem (if you think the status quo is a problem). Pick one or more of:
(1) Allow dropping prone as a reaction against missile fire (imposes disadvantage on ranged attacks and rewards a combined-arms approach with both melee and ranged elements, so the melee elements pin the enemy down with fire until the melee dudes can get there and clean up);
(2) Impose disadvantage on ranged fire if you use more than half your movement on that turn (makes it harder/less rewarding to kite);
(3) Making a ranged attack ends your movement for the turn (makes it even harder to kite, eliminates shoot-and-scoot tactics);
(4) Remove range limitations on monster abilities like Tarrasque fear and Medusa visage (eliminates a major defensive advantage of ranged combat);
(5) Disallow magic bows with nonmagical arrows from bypassing weapon immunities, and use more weapon-immune monsters (makes melee the only choice besides magic against these monsters; peasant mobs and archery won't work; magic still needs to be dealt with separately e.g. by introducing old-style Magic Resistance that lets you ignore spells);
(6) Halve the number of ranged attacks made (both cantrips and arrows) on the grounds that flicking a sword across a throat is quicker than nocking, aiming and firing an arrow into a throat;
(7) Use more monsters and more fast/mobile monsters like gryphons and dragons and earth elementals.
I was playing Master of Magic over last weekend and I noticed that it does #3 and #6 (melee units get twice as many attacks, and shooting ends your movement) and that as a result, while ranged units are powerful when they reach a certain critical mass, only heroes mounted on horses can kite truly effectively, and a ranged unit which gets into melee range of a melee unit is in bad trouble.