You can use in theory something other than /nix, but then you have to recompile everything yourself. So not many people do if, not sure about it’s state.
I just dipped my toe into the Nix pool a couple of weeks ago, and there are instructions to use root to create a /nix and grant ownership rw to your user account. No further admin required, but everything else seems to work as if using the Nix root user method.
The installer used to have an option for this, but nowadays it's discouraged. How come you wanted a single-user install so much? And j/w, are you on macOS?
Ok cool! The reason I asked is that the multi-user setup has more benefits on Linux than on macOS. That's because on Linux, the full build sandbox is actually available, and the store's immutability is enforced by default.
The tradeoffs are obviously yours to consider. But the normal Nix build sandboxing helps protect you from nasty things like crypto miners in setup.py or whatever, as well as improving reproducibility.
That's less relevant on macOS where the sandboxing story is not so great.
Personally, using Nix with a daemon seems like a better setup to me but adding another highly privileged process unnecessarily is obviously a real security concern. There is some ongoing work, btw, to reduce the level of privileges that the Nix daemon needs.