Encoding lag is not your only problem:
11:13:11.474: Output 'adv_stream': Number of lagged frames due to rendering lag/stalls: 360 (23.3%)
11:14:34.077: Output 'simple_stream': Number of lagged frames due to rendering lag/stalls: 533 (32.3%)
Rendering lag caused by GPU overload.
11:13:11.474: Output 'adv_stream': Number of dropped frames due to insufficient bandwidth/connection stalls: 394 (26.6%)
11:14:34.077: Output 'simple_stream': Number of dropped frames due to insufficient bandwidth/connection stalls: 799 (51.2%)
You dropped 26% of frames at 6000 and then increased the bitrate to 10K.
Frame drops caused by insufficient bandwidth.
11:13:11.474: Video stopped, number of skipped frames due to encoding lag: 453/1496 (30.3%)
Encoding lag.
I would say that, no, in a single PC setup, a 2080 is not able to do 4k60.
11:17:36.177: base resolution: 3440x1440
11:17:36.177: output resolution: 2580x1080
11:17:36.177: downscale filter: Lanczos
11:17:36.177: fps: 60/1
Downscaling would help viewers that didn't have enough bandwidth to watch 1440p60, but your machine is still trying to render 4k60 frames and then downscale them before encoding. Also, this scaled resolution, although it is lower, is still more work than encoding standard 1920x1080p. Your machine not only is not able to do this, it's not particularly close to being able to do it, as you're getting 20-30% of lost frames to both rendering and encoding lag, and the insufficient bandwidth errors seem to indicate you can't even successfully stream at 6000, which is what you'd be aiming for streaming 1080p60. So you're trying to push even more pixels than that; even if you could get the GPU to do the work of generating 3440x1440, if you drop your bitrate low enough to not drop frames, it'd probably look pretty bad.
That's aside from the question of how letterboxed the rest of the world without 21:9 monitors are going to see this.
