First, there are champions with larger win rates to look at first. Second, the only reason for her high pick/ban rates is that many other top notch adcs have been nerfed to shreds so her competition may be slightly lacking - she doesn't need a nerf so much as possibly some other adcs could use buffs.
Finally, as a Jinx main / semi-main, I'd say her lack of mobility is a severe weakness. She's very weak in lane. Not in the sense that in a 2v2 lane she'll lose (because she won't) but from a different perspective: her strength in lane is pushing power and yet her weakness is mobility meaning that she pushes and then becomes extremely susceptible to ganks.
Want to beat a Jinx? Pick an early game (or even just a regularly strengthed) jungler and gank bot lane at level 3. GGWP. A level 2 Jinx is dead from almost any gank or at least uses her flash (at least her Chompers can slow down a jungler enough to have a chance at survival). Once your ADC has a first blood lead on Jinx she can't push lane at all because they can beat her 2v2, and she isn't great at much else.
Jinx is also incredibly weak against non-adcs, particularly mid laners and junglers. While most ADCs have a dash/jump/blink/etc... she only has Chompers to defend with. Most mids and junglers have some way of bypassing her chompers quickly, thereby nullifying her escape potential. Having played Jinx against mid LeBlanc's I can say those games are miserable if LB decides to roam at all.
On a final note, in competitive play Jinx doesn't seem to see any picks at all, which is what the game is balanced around. I bet Riot would LOVE to see Jinx in competitive play, as her LCSBIGPLAYS ultimate would be amazing for viewers. Thing is, with the warding and team communication at high levels of play her ultimate is next-to-impossible (if not actually impossible) to hit from any range at all which pretty much defeats its purpose. Even outside of ranked 5s, if people have good map awareness and use wards they should be able to see her ultimate incoming. Add on to that the fact that her W has a massive indicator to make dodging it easy, her chompers have a noticeable (about 0.4 seconds) set up time, and her Q makes her choose between having the highest max rank basic attack speed in the game with nothing else, or having the lowest max rank basic attack speed in the game with splash damage and great range, means that she's always making a meaningful tradeoff there.
I don't think she's OP for a moment. Perhaps there are a few ADCs that could use some love and I definitely don't think Jinx needs help, but I wouldn't want to see her kit nerfed at all (maybe a small AS or AD nudge, but anything more would be uncalled for).