Possibly the thing that makes C be C is that there is only one C. It is the single lingua franca of "one notch up from assembly". I would argue any language that wants to be a better C has to accept the challenge of being available on any platform, existing or future, any architecture, suitable for any bare metal use case, and it has to want to be the single obvious go-to choice. That's what it means to step into the ring of "better C" candidates. A lot of languages might offer pointers, manual memory allocation, no runtime, etc. That's cool and that gets you close to the space. But if you want to be a better C, then the bar is much higher: ubiquity.
IMHO one of C's strong points is the ubiquity of non-standard compiler extensions, C with Clang extensions is much more "powerful" than standard C, personally I see C as a collection of closely related languages with a common standardized core, and you can basically pick and choose how portabel (between compilers) you want to be versus using compiler-specific extensions for low level optimization work (and in a twisted way, Zig is also a very remote member of that language family because it integrates so well with C).
> "one notch up from assembly"
C is actually a high-level language, it's only low-level when compared to other high-level languages, but much closer to those than to assembly. Arguably Zig is in some places even lower-level than C because it's stricter where C has more "wiggle room" (for instance when it comes to implicit type conversions where Zig is extremely strict).
> being available on any platform, existing or future, any architecture, suitable for any bare metal use case
Zig has a pretty good shot at that requirement, it has a good bootstrapping story, and for the worst case it has (or will have) a C and LLVM (bitcode) backend.
For me personnally, Zig will most likely never completely replace C, but instead will augment it. I expect that most of my projects will be a mix of C, C++, ObjC and Zig (and Zig makes it easy to integrate all those languages into a single project).