Coming from the broadcast world... On the occasions we have to deal with HDMI in high-end AV, it just seems totally crazy.

Without a doubt: SDI over coax. Mini coax will go 300ft. The thicker stuff can go further. It's fast, easy, and fairly cheap to terminate. Much faster and easier to work with than CAT6. Tons of very high quality routing and distribution products. Easy/cheap conversion to/from HDMI and fiber.

Return channels, bi-directional control, and even HDCP could be implemented if the industry wanted to. Lots of history of modulating additional signals.

I don't know the details of how JAP works, but keep in mind the following bandwidth requirements (all data must arrive on time):

HD: 1.5 Gbps
UHD/4k: 12 Gbps

Not sure how you can do that over ethernet without compression and some latency.