The same wires on the HDMI cable are used for HDMI ARC, which is far more useful to most TVs (as it allows smart TV apps to back-feed their audio to a soundbar or receiver "upstream" of the display.
I never needed to use it and I’m not sure what was the motivation to introduce it into hdmi, but requiring cooperation would explain why it wasn’t used widely.
Most devices didn't support ethernet over HDMI, and it was not something that could be passively supported.
> I never needed to use it and I’m not sure what was the motivation to introduce it into hdmi
The idea was that you could have your TV or AV Receiver connected to your normal ethernet and any other connected devices would just magically have network connectivity as well.
Turns out that most people who care to wire their home theater don't mind just using a switch to connect everything directly, and most of the world will just use WiFi if given the opportunity.
Also AFAIK it was limited to 100mbit/sec so by the time it became a thing it was already kind of obsolete.
Also, I recall reading that TVs from certain manufacturers had/has bugs in them that will prevent TVs from functioning after periods of time without connection or firmware updates.