I assume the intention is to run only a bare-bones OS + Proxmox directly on the laptop with all the other functionality virtualised or compartmentalised through KVM and LXC, managed by Proxmox. Running the desktop directly on the hardware does not fit this profile.

I'd say this - having nearly everything compartmentalised with access to the laptop display - might be possible by using containers instead of virtual machines. This would not work for Windows but it could probably be made to work for those mentioned Linux installs.