My argument for sticking with ELF Tool Chain strings is that we install it unconditionally and it gets used outside of traditional toolchain applications (e.g., it may be installed on more constrained embedded systems). In contrast to tools like nm, objcopy or even readelf where we need support for different formats (LLVM IR or different symbol tables, say) I think ELF Tool Chain strings is fully functional. Have you noticed anything missing from it, or is this just for consistency with the other tools?
On my laptop ELF Tool Chain strings is 16KB and depends on 103K libelf.so.2 while llvm-strings12 (from pkgs) is 30K and depends on 87MB libLLVM-12.so.
I updated this so it will install ELF Tool Chain strings, unless WITH_LLVM_BINUTILS is set, in which case llvm-strings will be installed as strings. It shouldn't change the current behavior of installing strings regardless of whether the toolchain was built (which I completely understand).
If WITHOUT_TOOLCHAIN is not set then llvm-strings will be built and installed anyways so I see no issue with installing it as strings too.