He DOES fall off (and hard), but only if you don't feed him.
You know what Draven has? He has high, but unreliable, auto attack DPS. That's it.
Stand Aside is a pretty mediocre utility spell, and Whirling Death (while not horrile) is still the worst global ult in the game.
He's got no poke, mediocre range, shitty CC, and low mobility. In an even fight, Draven will usually come on top, yes, but he can't make you fight him unless you fuck up and get hooked.
Look at what Draven has come late game.
His passive provides him with absolutely no advantage when everybody has their full build.
His Q still lets him double dip into bonus AD, but it's so unsafe to use it in a teamfight that it makes the already vulnerable Draven into an easy target.
His W is still a good steroid, but it relies on catching those Axes, which is dangerous late game.
His E is only useful for interrupting some mobility spells.
His R still sucks, even more so in the late game.