What you're describing is fully a product of the display controller architecture, not the digital signal. You can "chase the beam" with HDMI/DVI just as well (or better) as you can with analog. There's no need to buffer the whole screen and be even one frame latent.

I've done it in Verilog on FPGA, for example.

But we do so on our machines because that's how the GPU/display controller pipeline works easiest from a software POV. That latency would be present on a CRT as well. What would be missing is the internal latency present in some monitors.