Software-generated video is definitely difficult to get working from scratch, limited in resolution, and expensive in CPU cycles, but it's been done on several microcontroller families [1] [2] [3]. You generally still need an external resistor network to do the D/A conversion, though.

[1] http://www.rickard.gunee.com/projects/video/sx/gamesys.php

[2] http://www.theresistornetwork.com/2013/03/avr-vga-generation...

[3] https://hackaday.io/project/8537-vga-blinking-lights

Overall I think it would be neat to see a "hackable" (2D) video controller emerge too. There are quite a lot of "small systems" that could use with an easy way to get decent video out (practically speaking HDMI, or maybe DP).

A display controller that can drive HDMI and a 2D graphics accelerator are different things. They just both work from the same framebuffer in a SoC's memory.

A special chip isn't really needed for this, an FPGA can do all of the above (with the correct bitstream)

Fpga, discrete asic, or on-die on soc, that's just implementation detail. Of course I'd expect the first iterations to be fpga based, that's almost unavoidable these days.