The real reason Aatrox receives no buffs is because he can't be buffed. Aatrox is much in the same boat of Tryndamere, they're in a binary, locked state until a rework comes out.
Aatrox will always be better at splitpushing than he will at anything else, until they change certain aspects of his kit, such as his E. If they buff any aspect of Aatrox, without changing his kit around, his splitpushing has inherently been buffed. Buff his Q damage against champions? Now he dives someone in a tower that much easier, instead of diving on the ADC during a teamfight. But that's just an example.
The best way, in my opinion-as a rank 6 (Soon to be 7) Aatrox player, is to change up 2 of 3 things.
HIs E, currently, it does nothing but provide him a bit of damage, a slow to opponent's he's chasing down, and waveclear. This ability is typically leveled first for great reasons. He constantly harasses his opponent with it, he clears waves with it, it stops his enemies from running away, it stops them from chasing him. The biggest issue with it is how simple the ability is. You hit it or you don't, and if you don't, oh well. The ability's back up in 6-9 seconds anyway! I'd fully recommend replacing this ability for something else.
HIs Passive, Bloodwell is not helpful in getting Aatrox into a teamfight; It's great for getting him to stomp the enemy laner every 200 seconds or so. Again, it's so binary and simple, you have it or you don't, and if you do, jump on them and kill the enemy laner. If you don't have Bloodwell up, poke them first.
Bloodwell needs something to boost him during teamfights, if they want to move him over to the teamfighting role. Such as, the more enemies around him, his Blood Price becomes more empowered, as long as he has Bloodwell ready. If it is not ready, Bloodwell empowers his Blood Thirst. Just a suggestion.
His Blood Price/Thirst. You deal extra damage to your lane opponent, based on your AD, or you heal yourself, increasing that heal if you're below half health. It's so simple which one to pick, you either heal yourself if you can't out-DPS an enemy, or you burst someone down with Blood Price. This needs dynamics or mechanics to it, or even just simple changes. "If there's an enemy champion near Aatrox's target, Blood Price effects them as well." or "For each enemy champion Aatrox is near, he heals for 10 extra health"
If at least 2 of those three changes happen, as well as some increased base stats, Aatrox's role as a Diver/Split-pusher can instantly change to Diver/Juggernaut.
-Sincerely, an Aatrox player who really fucking cares about
being a teamfighting badass