As an OC'd to 4.4 (2c) - 4.2 (3c/4c) 3570k owner with a GTX 1080 in my system, I can tell you right now that yes, you lose about 0 - 20% of GTX 1080's optimal performance. Depends 100% on the game and your target frame rate but yes, there is a loss.
That said the combo still does well and I disagree with it being a bad fit for a 1080p monitor. If 1080p 60 hz then yes, no way you'll utilize either the CPU or GPU max performance, but if 120hz or up, then this is a well balanced rig.
@Ferrum Master is spot on - if you can push a 4.5 Ghz OC on all cores, then you can mitigate almost everything you lost. Its a feasible OC on a decent air cooler. and a half-decent chip.
We have pretty much identical systems, even same RAMs
Note that even though CPU usage isnt pegged at 100%, there are other bottlenecks in the pipeline, of which a big factor is RAM throughput, but also just the game/engine.
Also, you really need to OC this still pretty beasty CPU. You're running 3.8 Ghz now... moving to 4.2 all cores is a pretty big boost already and you can do this in many cases without ever touching the voltage. Another route you can take, instead of upgrading your whole rig, is to just go for a 1440p monitor. This will remove the burden off the 3570k and towards the GPU. Just give it a shot; throw a 42x multiplier on each core Turbo and leave everything else as is - if not stable, move to x42 on 3core active and x41 on 4 cores active (or more volts).
If you're unsure about safe voltages: keep core temperatures below 86-88C, and don't exceed 1.3v on air. If you want more tips for a quick n dirty OC, let me know ^^