USB4 uses something called DP-Alt where it’s actually DisplayPort over USB exactly what you’re looking for. I have a portable USB-C monitor that runs powered and video over a single connection

DVI isn’t capable of the bandwidth needed for higher resolutions. Even dual link maxes at about 8 Gbps and 2560x1600 @ 60Hz. This new HDMI spec is 96 Gbps for reference.

Ironically though HDMI is pin compatible with DVI and you could output HDMI to a DVI monitor with just a simple HDMI to DVI cable, or vice versa. I know a lot of people who like DP bit in order to convert you need active circuitry and that can impact quality if you don’t have native DP on both ends.