The real limiting factor here is that, assuming you could get a GPU with USB-C-out, you'd have to pass that power and any for accessories hooked up to the monitor through the GPU, and the nice ones currently are hitting the limits of available power already all by themselves (75W PCIE, 2x 150W power connectors - and a Vega 64, for example, can briefly peak at 360W).
So, to power your monitor over the same cable (and have at least another 15W for accessories plugged into it), you'd need a GPU that maxes out well under current ones on the market, which kind of defeats the point, you know?
On a side note, the way GPUs are increasingly hitting power constraints is why you see new designs switching to weird proprietary stuff like Apple's MPX modules, which allow a dedicated 500W per graphics card.
I would love to reach the point where a desktop computer only had a single power cable leading to the wall, with everything else getting powered via it.