5e could also do a much better job at having both high Str AND high Dex be useful somehow so it wouldn't always be either Str or Dex, but never both. E.g. the strong elven melee warrior archetype doesn't benefit from 16 Dex because of how armor caps Dex at +2 or +0.
Slightly off topic but imo D&D should go back to how it was in 3.5e/Pathfinder: melee weapons always add Str to damage, and ranged projectile weapons don't add any bonus to damage (like cantrips). Characters could get a feat - Weapon Finesse - that allows them to add Dex instead of Str to melee weapon damage, and bring back composite bows! This would go a long way to making Str less of a dump stat for Dex characters.
Also Str+Con should be a single save (Fortitude), as should Dex+Wis (Reflex) and Int+Cha (Will). This would make both Str and Int less dump stats.
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