There will absolutely be cases where the 9590 bottlenecks a 1080.
If you're only aiming for 60hz gaming (like a 4K, or 1440P ultrawide 60hz display), then the 9590 will probably hold up okay. I don't know of any games where it's not up to pushing 60fps most of the time, whatever the resolution. But if you've got a higher refresh rate display and you're looking to make good use of it, like 100fps +, there will absolutely be games where the 9590 starts to hold you back.
Here's GTA V:
http://www.techspot.com/review/991-gta-5-pc-benchmarks/page6.html
Even with a (Maxwell) Titan X - slower than a 1080), is showing up a CPU bottleneck on the 9590 around 73fps
Battlefield 1:
http://www.techspot.com/review/1267-battlefield-1-benchmarks/page4.html
There's no 9590 there, but you can see the minimum fps of the 8370 is miles below the 6600K & 6700K. Again, it's fine for 60fps, but if you're targeting more, it will become an issue in some games.
No fanboy-ism here. I'm cheering on Zen as much as anyone, but the brutal truth is that there is just no place for an AMD CPU in a high end gaming PC right at the moment.