I disagree. I changed my own system to Proxmox from Supervised for similar reasons your are facing. I’m not sure I would call installing an OS and then a VM an unnecessary overhead and don’t find any discernible difference in the way the machine operates verse previous, power usage is almost identical. I also changed the HA machine in my business to use Proxmox.
If you have experience in using Proxmox, I suggest you reconsider using it for HA to give you the flexibility you are looking for.
You could install in a venv, that way HA won’t be exceeding any imaginary boundaries 
If you could link to where Hass.io is referenced in any of the current installation instructions, that would be great. Someone can submit a PR to remove it.
Yes, the Devs have been slowly removing it from the code, it takes time as changes to that reference creates breaking changes in other places of the code, from what I have read.
Yes. Here is a great community document that details the current installation methods and names.
You will also see the current installation methods listed here on the HA website.