-Better split damage assuming no int/fai shenanigans (your choice of pure phys, holy, flame, lightning, rot, bleed, MAGIC AND FROST (see point 5) vs. phys, magic, frost (sometimes), lightning but worse, see point 4)
-Buffs to improve physical damage, fire damage, bleed, poison, and more than just simple weapon buffs- damage buffs (Flame Grant Me Strength, Golden Vow), heals over time, huge one element resistance incants. Certain buffs are on weapons' AoW so you don't need the slot for them.
-You can get a mainstay fth/str scaling weapon faster (Tree Sentinel Halberd/infusing a greatsword with Sacred Blade vs. Infusing a greatsword with Gravitas, Meteoric Ore Blade, or Clayman's Harpoon)
-Even if lightning doesn't scale with faith, your lightning incants can and so there's less pain when wearing Lightning Scorpion talisman. This is pretty much only applied to one weapon I've seen normal strength builds use- Great Dragonclaw.
-Potential access to dragon incantations, and thus Glintstone Breath/Smarag's Glintstone Breath, Rot Breath/Ekzykes' Decay and Frost Breath/Borealis's Mist vs Glintstone Icecrag/Freezing Mist, making the frost/magic damage advantage point moot in some cases. Similarly, there's also potential access to blood incantations, leading to bleed damage in your arsenal, although both of these benefits require investment into Arcane
-Night Maiden's is fine on specific low health enemies such as Crystalians, but hard to use as some are too fast to stay in the mist and isn't an Ash of War on any weapon. Godslayer DoT is basically the same except not in an area and has upfront damage, as well as a str/fth weapon with said DoT on an AoW: Godslayer Sword. (Less of a point btw as Crystalians are easily dealt with via a hammer/greathammer but I'd figure I'd add it to be sure.)
-Does not require Ranni's questline to be done for several weapons in the build.
Compared to str/int:
-Ashes of War available quite early (3 from Rogier, Gravitas off the Coastal Ruins)
-More consistent damage as there's not too much variety, only need Magic Scorpion talisman (except Stone Sling and maybe other gravity sorceries, unless you put in enough faith for Gelmir sorceries, then there's fire I guess)
-More consistent spells, Glintstone projectiles are very similar vs. Lightning Spear vs Fireball vs Flame of Frenzy
-Lots of big magic damage weapons to choose from with AoW aplenty, as well as a better infusable weapon than str/fth only having Erdsteel Dagger as an option. They're honestly even and it's personal preference for AoW but int has less body buffs and is more set and forget, meaning you can just use the weapons you want instead of swapping between multiple sets- also potentially saving in reinforcement costs. Gravitas/Alabaster Pull to suck in and damage enemies, Onyx Repulse if you want them to fuck off, Waves of Darkness (which could only be applied to Colossal Weapons iirc), Death's Poker cheese if you want to breeze by the early game, Starcaller Cry as a sidegrade to Alabaster Pull (due to speed) on dual greatswords, Troll Knight Sword's Troll Roar far earlier than the ash in Mountaintops, Wave of Destruction on a primarily strength Colossal Sword, Dark Moon Greatsword self buff with heavy attack projectiles that cost no FP beyond the initial buff that increases damage and frost build up as well, Wolf's Assault on a frost greatsword if you don't like Dark Moon Greatsword, and most importantly Clayman's Harpoon has innate int scaling/magic damage but can be infused heavy, magic or frost. Once you have the whetblades, you can make it anything with regards to your strengths.
-Rain of Stars can take care of annoying fast enemies, or Night Comet so they don't dodge (and again, if you do str/int/fai for some reason, there's Rancorcall I guess but you'd probably stick to two stats.)
-Better spells either are only int, or they're built for int/fai and shouldn't be considered in this kind of build, potentially saving stat points for more vigor/endurance/mind.
-Greatblade Phalanx deals massive posture damage, helps double down on one advantage of a strength build.