We (linphone) do H264 software encoding and reach 720 on high-end iPhones (5s and more). So 1080 should be doable in realtime with, say, 20 fps, on an i5 I'd say?
Depends on bitrate. I mean, my old Lumia 920 with a underpowered dual-core ARM CPU could encode 1080p at 10Mbits/sec from the camera module - really shouldn't be an issue for any modern PC to have video-conference quality video.
You're confusing hardware encoding with software encoding. Your phone doesn't do it on its CPU (or GPU for that matter). The camera module usually has a separate chip for the encoding.
Some of the speed comes at a cost of lower compression. Not that big a deal when it only has to got from camera to SD card, but important when it needs to get transmitted across the mobile internet in real-time.