Well, the other thing is her ult.
Think of it this way: say that you're Kass. Or Fizz. And you want to go gank a lane because yours isn't going well. You've got to either walk down there relatively slowly or you use your abilities to get down there faster. Now, there's no guarantee you're even going to get anything out of this, and chances are by the time you get there the opportunity you were looking for may very well have just passed you by. If you miss your chance, it's now a very long walk back to lane, and you're likely losing a lot of farm and tower damage to the enemy laner. Sure, you can still have this pan out very well and get you ahead, but there's an equal - or even greater - chance that it doesn't.
But let's look at Quinn - she calls down Valor, zips down to another lane much quicker and can now pick and choose when she goes in because she arrived there so quick. If nothing comes out about it, no biggy - it's not mana intensive to return back to lane and she can even do it much faster. Come mid-game, if she's behind still, she has all the mobility to basically farm all lanes - clear a wave, fly to the next, clear it, fly to the next. You can snowball your gold-lead just off of sheer map presence and mobility.
As it stands, a roaming support was one thing - a designated roaming champion with actual basically causes you to have two junglers, where one just happens to be in a lane. But it's at the point you can absolutely call on a Quinn to gank for you whenever and actually be able to expect her to have the capability. In the course of maybe four or five games I've collectively ganked my laners over 20 times - at least 4 ganks a game on Quinn on average. Why? Because it's so easy. Half the time the enemy laner can't even react to it unless they've had a ward in deep mid river, and asking laners to do that regularly basically asks them to lose farm and risk getting caught by the enemy team in no-man's land just because they're so scared that I may drop in for a visit.
Her damage is strong, her bullying is, too. They could tone that down and balance her out for a lane - but even so, I could still get myself and my mid-lane fed off of a few trips down the river, and the funny thing is that masteries even help me do it better.