I'm sure you could run Kodi on top of this, but then it would be just as restricted as any other app, and not be able to do the things I mentioned compared to running it directly via something like LibreELEC.

Kodi can actually run third party apps, for what it's worth: https://kodi.tv/addons/matrix/

But kodi is still an application with addons, Kodi is not going to allow you to run native applications on top of it

You can run native apps from Kodi.

I used to launch Steam games in Big picture mode from Kodi just fine.

Actually I was waiting for a desktop environment like this Plasma Bigscreen for a while but then got a new TV with Android and use that instead.

I would still prefer to use Kodi as the main app launcher on Android but it gets Killed to save memory and takes a while to start up again.

And using Kodi over HDMI is not an option anymore since a lot of content I watch comes in 4K 10bit HDR or 4K Dolby Vision and sadly desktop Linux does not support HDR and variable refresh rate over HDMI (so Linux Steam experience also bad).

Indeed, Kodi shines because it has native addons that make a consistent experience.

Everything is easy to drive via a TV remote.

The skin system lets you have as much UI eye candy as you like.

Chances are someone has made an addon for whatever you want to consume.

You're just running ye old HTPC otherwise.