I like the idea behind her as this "I could be anywhere at any time" champion. I think if they buffed her dueling potential a little more, she count easily stand shining as the go-to split pushing ADC. I think it's her squishiness that makes her ill suited as a split pusher anymore, which really puts her in a terrible spot.
Being forced to choose between defense or damage limits her ability to do anything against champions who naturally bring both to the table, which happens to be the core of the top lane meta with champions like Gnar, Illaoi and Irelia who are all really good duelist because of their combination of damage and tank.
In that situation where she's ill suited for top lane, she'd be forced into either ADC or possibly as an AD mid laner. Unfortunately with her lackluster auto attack range, it makes her ability to stand as an ADC much harder. Especially against really aggressive poke lanes like Caitlyn, Jhin or Ashe who are all some of the most popular picks. In the mid lane, while she has a good amount of burst, she can't deal it out fast enough to deal with other mid laners who are both burstier and have hard CC in their kits.
I think the only decent spot for Quinn right now is the Jungle, simply because it limits her interactivity with laners who can poke her down, zone her off of farm and inevitably shut her down because she ever has a chance. Not to mention she could gank all 3 lanes in the span on 60 seconds as well as know if it's safe to engage in the first place by using her W just beforehand.
She can pop up anytime from anywhere in the jungle and be ganking a lane super fast. Faster than where the typical ward locations won't give the enemy laners enough time to get out before she's on top of them. Unfortunately jungle Quinn has the same problems as Shaco wherein if she gets set behind by either strong counterjungling or failing to secure kills or worse, getting 1v2'd while trying to gank a lane, she becomes absolutely worthless for the rest of the game, useful for little else than being a mobile ward.