Okay you should have clarified that in your original comment, it's not that Nix is incompatible with unprivileged containers (it includes built in support!) but only with a specific container system that isn't even the most popular one (Docker AFAIK).

As for why those paths have to be hard-coded: they don't it's a config variable you can change. When you change it you give up using other people's binaries so you have to build everything yourself, which is exactly like every other distribution system that relies on hard-coded /usr/whatever paths for binaries. The FHS standard is incompatible with Nix's guarantees and dropping it is where it gets all of its power, so it has to use something different, and it chose to make that path /nix/store/whatever