You may instead by remembering the fact only some TVs back then were successful at powering the Chromecast without an external power brick, using a USB port on the TV itself to power up the Chromecast.
In applications where this worked (and it often did work, although it also often did not work), it could provide a solution that existed entirely on the back of the TV with nothing additional plugged into the wall.
But it was still [micro] USB that provided the power to the OG streaming stick, not HDMI.
It is not - I still use my 11yo Chromecast Gen1 today. And it still works fine without USB power (as long as you don't try to play YouTube videos).
This is probably not my most grand of deeds in my two hundred and seventy years, but it is nonetheless the most memorable to me on this fine Saturday morning.
I'm looking at my first gen plugged into the ARC HDMI port on my Vizio TV. It is ONLY attached to the HDMI port and nothing else.
Maybe because it’s NOT a smart tv and doesn’t have some crazy android chip SoC to constantly power. I mean obviously you can make a power supply that could do both - or neither. But it likely comes down to price for the manufacturer of the tv
I had the same first gen Chromecast (may even have it lying around somewhere) but it came with explicit directions to use the included power cable, so maybe they updated the included guide some time after release.
It's possible yours didn't provide enough power via HDMI, but at least ours worked just fine.