(no...no...NO! I went back a page rather than delete something...aw ^#$@, let me type it all again)
This I'm going to outright disagree with. I played the Draven a TON so I know how he plays. And one thing I know is that his old Passive really was satisfying, and not because it was OP, but there is a certain gratification with seeing your enemy's health slowly flicked a bit over time whenever you hit them with a spinning axe. That's some of my favourite thing to see in LoL.
Then again I'm also huge fan of Liandries, Swain's DoT, Teemo's poison, and Brand's Passive(too bad I hate everything else about him). So maybe I'm just a DoT type-a-guy.
Anyways, another thing you got wrong is the assumption it encourages aggressive play. Draven's passive does NOT make him play more aggressively. The way he plays with his new Passive is how he was played with his old Passive anyways. You should always be avoiding death as Draven. You should always be catching axes when it's practical to do so. You should always be dealing damage. And as the ADC, you should always be getting kills if it's possible to do so. Stating that his new Passive promotes an aggressive Draven is a misnomer. In fact, I'd argue it encourages player to play more defensively as dying means they lose their hard-built adoration.
The biggest issue with this Passive is that unlike most abilities, Draven's Passive actively makes the player feel WORSE. Getting a kill often makes you feel elated, but your Passive can also lessen that elation when it triggers depending on your adoration stacks. If you were recently killed(which isn't hard with Draven), your next kill is going to be a lot less satisfying than a normal kill even though you technically got more from that kill than any other champion in that game. Other times you kill a champion and realize that you haven't built up too many stacks because your ass is getting kicked and your lane is getting zoned, and that makes you feel like you don't even have a Passive. And here is the worst part. Dying in LoL feels shitty enough as it is. Draven's Passive manages to make dying feel far shittier than it already is. There are very few circumstances that can make dying feel worse. Giving enemy double buff, dying as a stacked Cho'gath. Dying with max Mejajs/Occult blade. With Mejaj and Occult, no one in a serious game ever buys them. With buffs and Cho'gath, while they feel really shitty, they make up for it with amazing pay-off. Infinite mana and ability to spam abilities for having it in the first place is an amazing thing. Growing in size and gaining a buttload of health is a great pay-off. Draven's on the other hand requires you to slowly build it up for a few minutes before it can even be considered a pay-off. And even then it doesn't really feel all that great, especially in late game.
Maybe it's because I often hate gold-based abilities outside of TF's consistent Passive. Maybe it's because I was rarely ever a fan of abilities that only procs on champion kills outside of those that reset ability CD's. But Draven seems to be, by far, the most frustrating Passive to have. It feels half-baked. In fact, I think my theory that it's a rushjob IS correct, they didn't even bother making an icon for it.
tl;dr: DoT passive with satisfying. New passive doesn't encourage Draven to be more aggressive than he already is, and sometimes may have the opposite effect. His new Passive actively makes you feel WORSE. It feels like a half-minute rushjob so they can go along with newer more exciting projects like balancing champions more people actually play.