Or just properly learn how Docker works, which doesn't really take that much time
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.
I think adding a package manager would mean more work than you think. You can't just plug-in a package manager from a different distribution and use their package repo.
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.
packaging - Can Guix packages be delivered to other distros? - Unix & Linux Stack Exchange
I can't be sure, but it seems to be easy...