People who say that at higher settings the CPU doesn't help have no idea how games actually work.
I personally guarantee you that whether or not your FPS increase by a sufficient margin, your games will become much smoother and more enjoyable.
Back in 2005 in NFS MW people used to say A64 @ 2.4Ghz was enough, I had a 1900xtx and couldn't enjoy until I upgraded to a Core 2 Duo later, C2D at stock.
This was a game released when dual cores hadn't hit the market and according to people didn't even use 2 cores much.
So rest assured you will see a huge increase in minimum FPS and whether or not that increase is impressive, your games will become a lot smoother and the experience will be better.
I had read somewhere that a guy went from a 2600k to 3930k, the FPS were more or less the same but the smoothness was noticeably more in the 3930k setup even when the game was only using 4 or less cores.
So people who say otherwise haven't tried each PC with each configuration and played games personally on each setup.
From experience I can tell you that a CPU is at least as important as the GPU and the GPU basically helps with FPS, the smoothness comes from the CPU once the average FPS are in place.