AFAIK Framework Desktop supports CEC on motherboard’s HDMI 2.1 port on hardware level (the only PC I know to do this, besides Steam Machine). It is not enabled in firmware though. The main reason (again, AFAIK) is that the Framework team does not see this as a high-priority task.
The availability of the feature on the hardware level was discussed in other forum posts (see comment above). Even Framework team member joined the discussion at some point.
P.S. I agree with everything you say, except I believe that HDMI CEC feature should be controlled through EC interface.