IMO, draven does need something. The dmg draven does doesnt really compete with the other adc's in his class. When you add in the fact that jinx can in fact out dps draven despite having more range available to her, then the case that Draven just cant compete with anyone in the class of immobile adc can become very strong because I would say that both twitch and ashe can out dps him as well.
I would say that people drastically overestimate his dmg. One "draven main" I talked to believes that the spinning axe dmg crits. It simply does not crit. Theres a perception gap I dont really understand. Ive heard that draven can 6 shot any tank in the game. How? The spinning axes add a maximum of 300 dmg. With 300 armor, thats equal to less than 100 dmg. Thats really nothing to write home about.
Continuing with perceptions vs reality: Before the kog rework, I would find myself standing still in a fight and giving 8 autos without needing to reposition, whereas even 1 auto with draven incites a reaction form the enemy. We can all agree that kog does more dmg tho right?
I think draven is flashier, and gets more attention, and projects a distorted image of his actual capabilities which are not that impressive in reality. Dont get me wrong. His passive is a bit absurd and he can carry a game with ease. Hes not like unusable or anything. But like the OP said, he is under-performing. ESPECIALLY when you consider that his passive is about snowballing, and we are in a snowball meta.