The 8700K is enough to run twin 1080s in SLI.
The "no bottlenecks" part I think is a stretch because all systems have a bottleneck. The bottleneck is simply the component that's preventing you from having higher performance. If you upgrade your bottleneck, you get better performance. No gaming PC has infinite FPS, therefore every PC has a bottleneck.
Your question cares more, I think, about whether the bottleneck would be the monitor, the GPUs, or the CPU. It could also be something like the RAM or if you're playing multi-player games then your ISP. You'd have to tell us what monitor you plan to use in order to give a sense of whether your proposition is reasonable, overkill, or will not let you use your monitor fully. For example, a single 1080p 60Hz monitor - this is overkill (ie, the monitor is the bottleneck), but a setup of four 1080p monitors at 144Hz is the same as 4K @ 144Hz which you won't be able to drive in many AAA games (ie, the CPU or GPU is the bottleneck).