Still the big image size problem, but maybe you're right...
Linuxbrew vs guix? Guix is full ready to use for linux. Compiled packages already done.
Binaries are available for Linuxbrew as well, called "bottles".
Theoricaly, it is as simple as it seems. If you want to install guix on a distribution you need 1 compile it, 2 enable the deamon. And then you can install what you want in userspace with shared libraries instead of root system space overrides.
Practically, you're wrong. LibreELEC doesn't have fully fledged util-linux, but uses instead busybox. There's no bash. There's only a root user and not possible to add users. There's a read-only root system. I understand that you can install GUIX in a separate location, but I'm quite certain that you will run into issues with the mentioned limitations. The binaries themselves will run, but the daemon and scripts to start etc will fail. Come to think of it, Linuxbrew will probably have some issues as well.
I do agree though, LibreELEC desperately needs a proper package manager. Personally I have tons of tasks for my living room HTPC. Most of them unrelated to Kodi.
Flatpak/Snap might be better alternatives. Someone should look into packaging one as an addon (or simply integrated into LibreELEC). I might, but probably not in the near future.