I copy paste what I said in an other comment (TL;DR, you compare apple to orange):
Their kit are extremely different, I can't compare Urgot to Aatrox in this sense because their whole kit have different function/gameplay.
What I mean is that I play aatrox, played him on PBE and a bit on live, as someone who main Urgot and who also played poppy quite a bit top, your complain doesn't make sense. You need to work around your window of power, Aatrox passive is massive and it is YOUR JOB to find proper way to use this very strong dmg output who have an improved grievous wound.
You say "Aatrox get nothing" but aatrox main dmg input is in his Q for example.
Urgot work differently because his whole kit is balanced around his passive which is his damage input and what make him a mid game monster.
Poppy have this passive to get stronger laning phase and trade, while her kit is a mix of... warden/bruiser work.
Aatrox passive isn't what make his laning phase, it is a trading tool that you use during your trade.
you get nothing on killing a minion because the reward is freaking HUGE landing his passive, it is a BIG chunk of damage and healing reduction coming with his Q damage.
What you guys ask is that the dude permanently get a free trade every 25 sec XD A trade that FUCK UP SHIELD AND HEAL XD So you can't even like think "I play Riven, I come take this CS and immediatly E to tank his passive" because his passive HURT and have a natural property to allow him to win sade trade with this. It is call "window of power", it isn't that hard.