USB-C in DisplayPort Alt mode plus USB 2.0 signalling for the keyboard and mouse inputs is starting to be a pretty common option on consumer systems. Capturing that would allow remote control of a PC including the BIOS using a single cable (though a second cable would still be needed for connecting to a desktop motherboard's header for power and reset buttons).
I think there just aren't as many options for DisplayPort capture chips as for HDMI/DVI capture.