Firstly, don't get Guinsoo's on Aatrox, tbh. The ap scaling isn't worth wile on him, and the attack speed ramping up is made null and void when his passive procs, it also takes up a valuable item slot that could be lifesteal or health/a better attack speed item.
I have 5 ranks of mastery on Aatrox, and I have to say, SO many people play and build him incorrectly.
He works well with items that give attack speed and defenses, and lifesteal. You basically build Hydra or Bork (Depending on the enemy team) then usually get Wit's End, Spirit Visage and the rest is situational.
He's super self reliant. He's squishy because he isn't a normal tank by any means. He is a sustain tank, you have to play around his sustain over his resistances. Jungle Trox is harder than Top because while his ganks are strong, but they take some practice to pull off successfully.
Mid game+ is where he's relevant, you have to abuse his power spike of 6, 11, and 16.
The W heal should only be good at low health, otherwise there'd be no reason to use Blood price.
He has bad scaling because his power lies in using his abilities effectively to allow the Trox to his auto attacks consistently.
His E damage is strong for it's range and slowing power. The width just takes time to get used to, and I honestly rarely miss with it. You can often combo it with your Q, and you can easily hit someone who's in your face with it by throwing it 45 degrees in either direction of them.
Sated + Guinsoos is an honest waste of item slots. Sated is definitely his best jungle item, but don't just farm the whole game until you get it, abuse his amazing gank potential. (Dive potential, 2 cc's, sustain.) But then get something that isn't attack speed and increases the strength of his autos. Like Hydra. (Hydra is practically core on this guy).
Low base health because he has infinite sustain and 2 lives...
He has cast times because otherwise his combo of sustain and damage usually wont be interrupted, and he would just gromp through teams. The best Trox players can usually use his cast times well enough to make it worth it. His Q increases his time he'll be hitting someone total, and his E keeps someone in range, meaning he'll hit them more. Both of these times are worth wile.
The R damage is massive, for what it does. And it also isn't there for the damage, it's there for the stats, increased range to keep someone in his auto attack range, increased attack speed to deal more damage/ increased sustain. His Q and E combo into his ult to make it so no one can escape him without popping some important cooldown.
Many people believe he just farms the whole game then comes and helps his team, but it isn't true. If your Trox is doing that then he is a bad Aatrox player. Aatrox's power spike relies on his ult and passive, if either of these are up, he's incredibly strong.
Practically unkillable unless 2 people waste their burst on him, which is a complete waste, as then his team smashes in. If his passive is up, it's doubly wasted.
His W does not consume so much hp if you build 1 lifesteal item. He heals for almost 1.5 times the damage it deals per two auto attacks with just Rav. Hydra.
The Q is slow, but good usage of it defines a good Aatrox player. The other thing is his W usage and timing.
Aatrox is SO strong in the right hands. I have played games where I didn't get fed, and helped in a team fight. The enemy team often underestimates his strengths, and doesn't realize they need to at least do something to get him out of Blood Price. The next fight I had dragon and 3 enemy team members attacking me while I had a Nami on my side. I Pressed Massacre and had Blood Thirst on, I stayed at a constant 40% health.
His biggest power spike in the game is after getting an attack speed item and getting a lifesteal item. Once you get some health you should be fine for the rest of the game once you've learned how to manage his abilities properly. He has the biggest "Make the right choice of abilities to use or you lose the fight" of any champion I can think of. Sometimes minimalism is the best option when they are fighting back.
Edit: BTW Aatrox is a juggernaut. He builds health over resistances and deals dps damage over burst while being very hard to kill and with a really strong mid-late game. He- like all juggernauts- make it less worthwile for people to deal damage to him over carries, but they need to keep him off their faces, or he loses.