I really don't think it would be worth getting a 2080 just to run games at 1080p with low settings. As far as performance goes, a 2080 should offer more than double the graphics performance as a 1060. Even if you ran games at their highest settings at 1080p, you would typically be limited by CPU performance more than anything, so reducing settings wouldn't really provide any significant performance benefit. Typically, graphics settings affect load on the GPU, and don't affect load on the CPU much, so there's not much point in lowering them with such a high-end card.
What kind of monitor do you have? Does it have a high refresh-rate like 144Hz, or just a standard 60-75Hz vertical refresh? Keep in mind that your monitor can only redraw the screen as many times per second as its refresh rate, so frame rates well above that will largely go to waste, aside from reducing screen latency slightly. If you don't have one already, getting a higher refresh-rate screen could be a good idea to go with a high-end graphics card. And you could probably get away with a slightly less high-end card, as even a 2070 can offer close to double the graphics performance of a 1060, while costing a couple hundred dollars less than a 1080, and even that could arguably be considered overkill for 1080p.
Technically, they "recommend" a 650 watt PSU, going by the wording on their official product page for the 2080. I suspect that a quality 550 watt PSU would likely be perfectly fine as well. Also, it looks like that's the locked i7-7700, which only has a 65 watt TDP, rather than the unlocked 7700K, and it's only a quad-core with Hyperthreading, so the power draw of that and the rest of their components should be fairly low. I would be surprised if the total power draw of that system's components ever hit 400 watts, even with a 2080.