Dex is a good stat, but I don't think strength needs this kind of help. Dex gets decent melee options and the best ranged options, while strength gets the best melee options and decent ranged options. I haven't seen a big movement among my players to drop Str in favor of Dex.
OTOH, if you'd be happy to let Dex apply to greatswords and glaives, then sure, let Str apply to bows as well.
DEX also gets initiative, AC, and a frequent saving throw.