Absolutely not. Nix and Guix are package managers that (very simplified) model the build process of software as pure functions mapping dependencies and source code as inputs to a resulting build as their output. Docker is something entirely different.
> they’re both still throwing in the towel on deploying directly on the underlying OS’s userland
The existence of an underlying OS userland _is_ the disaster. You can't build a robust package management system on a shaky foundation, if nix or guix were to use anything from the host OS their packaging model would fundamentally break.
> unless you go all the way to nixOS
NixOS does not have a "traditional/standard/global" OS userland on which anything could be deployed (excluding /bin/sh for simplicity). A package installed with nix on NixOS is identical to the same package being installed on a non-NixOS system (modulo system architecture).
> shipping what amounts to a filesystem in a box
No. Docker ships a "filesystem in a box", i.e. an opaque blob, an image. Nix and Guix ship the package definitions from which they derive what they need to have populated in their respective stores, and either build those required packages or download pre-built ones from somewhere else, depending on configuration and availability.
With docker two independent images share nothing, except maybe some base layer, if they happen to use the same one. With nix or Guix, packages automatically share their dependencies iff it is the same dependency. The thing is: if one package depends on lib foo compiled with -O2 and the other one depends on lib foo compiled with -O3, then those are two different dependencies. This nuance is something that only the nix model started to capture at all.
That means unlike Gentoo, I've never dealt with a "slot conflict" where two packages want conflicting dependencies. And unlike Ubuntu, I have new versions of everything.
Pick 2: share dependencies, be on the bleeding edge, or waste your time resolving conflicts.