The flip side to your purely technical viewpoint is exactly why the industry created HDCP. The 'perfect' data transfer method (w.r.t. analogue copying) that you see as a major benefit is a potential disaster that would enable recording and redistributing of near perfect copyrighted sources.

There isn't a compelling technical reason why a PC couldn't have an HDMI in, it's all legal. The industry would never sanction raw HDMI signals to be read in by an unrestricted general purpose computer. It would be equivalent to no DRM at all enabling you to record high definition copyrighted material.

I know that dumping to disk is different than actually reprocessing the signal to splice it into an immediate output, but i don't think there's much of a difference there.

If all you really want is PiP, look for a monitor that supports displaying multiple inputs simultaneously. This isn't a feature that should require a PC.

I'd love to live in a world where actions such as recording and storing weren't punished just because distribution is a protected right in some countries.