You said Arch can do “literally anything” that any other distro could do, and I’m trying to point out that by having to issue imperative command(s) to set Nix up on Arch, you’ve already conceded that the entire state of the system is not able to be declared in a config file, which is one of the features of NixOS. So there is at least one thing that NixOS can do that Arch can’t. I imagine there are other examples (and not only when comparing with NixOS). So again I ask, can you please refrain from hyperbole?

No, because while that lets you use nix to manage some of your packages, it’s still fundamentally limited by being hosted within the imperative Arch install. See for example section 2 in the very link you shared, which talks about starting the nix daemon at boot by messing with your systemd config.

I love Arch but I’d caution you against hyperbole like this. For example, NixOS has a declarative config for the whole system along with atomic builds that can be rolled back or switched dynamically. Not aware of any way to do any of that in Arch.