HDMI isn't used for data transfer
If HDMI has a really high Gb bandwidth and is readily available on most computers, how come its not used for data/file transfer?
HDMI was designed for for packet streams (video) and not data blocks.
While it is theoretically possible, especially as they’ve got a separate pin designed for Ethernet data transfer, no drivers exist that would enable this to work between devices (and most don’t have the correct ports.