HDMI is simply too thick. I can't see this happening.
There's mini and micro HDMI, but then you've gained nothing over USB-C.
Have you seen the thin HDMI cables? I use them almost exclusively now. Also thin ethernet cables.
Mini/micro-HDMI are plenty slim enough.
Good point.
Most people are going to be using this for presentations or for connecting to a TV. If you're going to need an adapter since most cables are full sized hdmi, then why not just use an adapter from usb-c?