That's exactly my point. He needs to find out if an upgrade will actually help him, because I upgraded from a 650 Ti to a 1080 only to find out I only gained like 15fps in WoW, until I upgraded my CPU (and then later overclocked to 4.6GHz) and finally boosted my fps from 70 (in 16:9) to well over 100 (in 21:9). You're right it isn't the hardware's fault, but how often is a game optimized perfectly? Almost never, especially in the first few months.
Another problem I faced which was fixed when I upgraded the CPU was fps drops in Fallout 4, which again were fixed when I upgraded the CPU. I would be happily running along at a happy 60fps and then boom all of a sudden drop to 50 fps, a very noticeable stutter. Went away completely when I upgraded that little bit of CPU, granted I also upgraded the RAM with the MB, but still.
All I am saying is you will be fine for the most part... but don't be shocked if you experience any difficulties. Because yes any CPU can bottleneck any GPU under the right circumstances and in certain situations some games will not run perfectly unless you also upgrade the CPU, the 3770K overclocked is only 15% slower than the base 6700K, but I experienced a WORLD of difference when I upgraded. And seeing as how there is only about a 5% difference between a 3770K and a 4770K and a 35% difference between the 1080 and the 1080 Ti I am letting you know you probably will run into problems at some point or another, and eventually you should look into upgrading the CPU. I know it doesn't sound like much but literally all my gaming quality issues vanished when I made that 15% jump from my 3770K to a 6700K.
Take some actual advice from someone who has actually been in your shoes... I know what I am talking about here. I lived it.
Like I said you should be fine for the most part, but you CAN and WILL run into issues with something eventually unless you are very lucky.
I'm not particularly saying you shouldn't get it or that it won't be awesome, but don't get your hopes up thinking everything will run completely perfect all the time, because that's what I did when someone said, "YEAH THAT'S AWESOME GO FOR IT BRUH!" when I put my 1080 in my 3770K system. No one warned me of bottlenecks, but guess what? in at least 4 of my games it bottlenecked and I still had to upgrade my CPU in order to play the games where I wanted to play them, (60fps 2560x1440p Ultra, now 3440x1440 21:9 @ 100fps Ultra)
No, I am letting you know you can and still run into issues, so you can be prepared for them and don't get mad and be like "THEY TOLD ME I WAS FINE."
And my 3770K was overclocked as much as I could get it on a liquid cooler, the same one I have now that is cooling my overclocked 6700K at 50C max.
Just saying.