I have an RX480 (which is roughly equivalent to the GTX1060 6GB), i5-3570K, and a 1440p 144Hz monitor.
Some/many games will run fine at medium-high to high settings. On others (Rise of Tomb Raider for example, which is admittedly pretty demanding) I had to run it at Medium just to maintain 55-65FPS. However, with variable refresh and LFC, it didn't/doesn't bother me much to be in those lower ranges.
Here's the way I looked at it. I had a 1080p monitor when I bought my RX480. I bought the 1440p about one year after that. RX480/GTX1060 6GB are not 1440p cards, but my monitor is going to last me through my next couple GPUs and I can afford to spend $300-$400 on a 1440p "capable" GPU now. Also 1080p on 27"+ size monitors bugs me because the ppi drops below 92ppi (equivalent to 24" 1080p density). 27" 1080p/1440p seems to be the tipping point for most people.
Staying with 1080p will keep your GPU costs down in the future though!
Don't want to beat this horse to death, but if you have any other questions, I'm happy to help (since I have a very similar setup)