The important part in Zig is that you don't need another compiler toolchain to build a mixed C/C++/ObjC project, how that's implemented under the hood (e.g. embedded clang vs self-made compiler) is an implementation detail.
I'd argue that C++ and ObjC support is just as important as C support for real world projects (because a lot of important libraries are written in C++ unfortunately, and ObjC is needed for calling into macOS system APIs - although this could also be done more awkwardly by going through the ObjC C runtime).
The one big downside of embedding Clang and the whole of LLVM is the compiler's executable size (somewhere around 170 MB).