Wherever there's such overlap, those dependencies are already shared. Static linking in such a situation means more disk usage, not less.
Packages in Nixpkgs have large closure sizes for entirely other reasons, like not splitting packages as aggressively as they could be split, or enabling/including most optional dependencies by default. Distros like Alpine typically lean the other way for their defaults.
It's true that if you're willing to manually mangle them, static binaries are nice because you can very easily strip all docs and examples or even executables that you don't need, and still know your executable will have the libs it's linked against. In one place at work I actually do this with Nixpkgs— there's a pkgsStatic that includes only statically compiled packages. I pull just the tiny parts of some package I need out and copy them onto a blank OCI image because it was the path of least resistance.
But Nix also has some really nice tools for inspecting dependency graphs to figure out why large packages are getting pulled in. nix-tree is my favorite, but there's also the older nix-du that gives the same info via graphviz instead of the terminal, and the built-in `nix why-depends`.
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Edited to add: wait, are you saying you used some other base distro to create Docker images where some things were supplied by Nix and others came from the base distro? If so, yeah, Nix is going to bring all the dependencies along, all the way down to libc or whatever. That's required for the kind of hermeticity that is its goal.
Mixed images like that are always going to be larger. But you also don't need a base distro at all with Nix. You can use one of the existing Nix libraries for Docker/OCI stuff to generate a complete image from scratch, or just copy your Nix packages' dependency closure onto an empty image with a FROM SCRATCH Dockerfile.
If you can't do that, you can do various things to try to slim things down but it's best to just Nixify whatever other packages you're using so you don't need a base distro. (And if you're trying to save space, Nix itself doesn't need to be in your Docker images either, which can also cut out some deps.)