bystander :
Another possibility is the PSU can't keep up with the increased power usage. That should show up if you monitor the clock rate of the card when gaming. You should also run a benchmark, like 3dmark Timespy to ensure it compares to the scores others get.
Sorry to say, but CPU, especially at 4k, have barely any impact over the result in many games especially that nowaday, these games are developed mainly toward GPU render due to consoles.
Upgrading my CPU or OC it will have barely any impact over the 3% margin which is insignificant.
As for power, I have a 1000W platinum power supply that was feeding double 290x in crossfire... I think it can handle a single 1080 GTX.
Temps are at max 64C because I make the fan goes at 100% around 60C when OC. And I also have a full tower with optimal airflow and 7 fans. Cooling is not an issue.
Issue here is even if I am playing a game with higher FPS, the framerate get choppy. When I don't OC my card, FPS is barely lower, however the framerate is smooth. I will check something and post again soon.