I'd imagine this solution inherits any problems that pacman has. The Arch wiki states that "if two packages depend on the same library, upgrading only one package might also upgrade the library (as a dependency), which might then break the other package which depends on an older version of the library." (https://wiki.archlinux.org/index.php/System_maintenance) This is one of the problems Nix does not have by design; in fact Nix lets you mix and match packages painlessly.
This also doesn't seem to allow unprivileged users to install packages, which is kind of a side benefit of using Nix.
Docker-esque solutions' issues with reproducibility are well known; I look at https://godarch.com/concepts/images/, particularly how packages are installed:
#!/usr/bin/env bash
pacman -S steam --noconfirm
and I see the same issues that https://blog.wearewizards.io/why-docker-is-not-the-answer-to... warns of. Heck the author even admits this is the case in an adjacent comment: "I want a machine that can be declared and rebuilt deterministically (at least semi-deterministically, rolling distro and all)" (emphasis mine).Also, frankly, I don't want to run my personal computer like a server, with complete immutability and the need to build fat image files every time I want to try out an additional program. That seems to me like a workflow that's better suited for servers where spending a few minutes for a deploy isn't a blocking operation, and where stateless service design is considered best practice.