I can see a maneuver or a trick that allows you to occasionly find an opportunity and modeling that by an int or cha attack.
Remember that D&D combat does not resolve individual swings, but rounds of combat, so 1/round is 'occasionally,' in a realism sense.
I can even see a system that tries to integrate all stats into a combat roll (Terrible design for a tabletop game IMO, but hey...)
It's been a perfectly good design for systems that go that way, they just simplify for playability in other areas. For instance, if a game has no mechanism that would force you to frequently re-calculate you attack chance, then the burden of factoring multiple stats in is relatively light.
I can't see a non-magical based way to constantly fight with int and cha instead of strength or dex.
There's no realistic way to fight effectively with just the abilities represented by a single stat. Picking one is accepting reduced realism for other design benefits.
STR as the governing stat for combat - and armor as the primary defense - was reasonable when D&D started out modeling medieval combat, and the only classes were fighter, cleric & magic-user. Then they added the Thief and the game struggled (not very hard) for decades to model combat styles that depended more on DEX. 3.0 did that first, 4e did it for every stat, but 5e has done it best, imho, by simply basing it on weapon choice (it's seamless that way - unrealistic, but seamless).
What's being proposed here is just an extension of that. If you can picture a stat as the determining factor in resolving a round of combat, then sacrificing realism to simplify it down to being /the/ attack stat for a PC that emphasized that sort of combat is reasonable.
You can see a 'feint' relying on CHA (deceit) to resolve a round in favor of one combatant (hit), but you don't have to assume a feint /every/ round. Just some of the rounds that that combatant hits. Most rounds that he misses, he didn't feint, at all (there was no opportunity). Some rounds he hits, he hits without needing to pull any tricks like that. You can even create a rule of thumb for yourself to determine what's going on, consistently. For instance: if you've got a character that use CHA for attack, and his CHA is 18, while the higher of his DEX or STR is 12, that's a +3 difference he's getting for using CHA. If he hits exactly or with one or two to spare, it was a feint or similar CHA-based combat trick that was critical in making that happen. Otherwise, it was a more mundane hit. He only actually feints occasionally. You could take it further: compare his CHA to the target's WIS. If CHA is higher, expand the range of hits that indicates a successful feint, if WIS is higher consider a miss by that difference an unsuccessful feint. You can go into more and more detail that way, until you have a deterministic system to model exactly what is realistically going, on instead of using any imagination, at all.
