Hachiko, the reason why attack doesn't trump strength despite needing 4 STR for every 1 attack is that the equations regulating damage done is affected in other ways. The damage we do is not simply drawn from one stat such as Attack.
In FFXI the "damage floor" was typically calculated by the player's STR and placed against the monsters VIT. The difference would affect the base damage you were able to do versus a monster.
Once you knew the base damage you could inflict, you then had to calculate the player's attack versus the monsters defense rating. This allowed you to modify the base damage by some multiplier.
That's kind of how FFXI worked but of course they had a lot more factors thrown in to compute the final damage (weapon damage for example, STR and Attack caps, etc).
I would imagine FFXIV is adopting their damage equations similar to what FFXI had. To be able to predict what kind of damage we can expect we'd have to throw in ALL the factors that influence it, which can include weapon damage, player level, elemental bonuses, STR caps and attack caps etc etc, the list can go on. I think it'd be great if SE can help us delineate that list of factors out a bit more.
+1 to the OP