So why would I be interested in Zig rather than Rust, if I'm trying to replace C code with something safer and more modern?
If this were generally true then C wouldn't be used in numerical applications which is clearly not the case.
I think this is the wrong way to look at it. Where C still has advantages over many languages is where the developer's primary mental model is the machine the program is running on. That's why it's used for device drivers and low level library work.
Over the last couple of decades, C has become less and less good at this task as the C model and the machine have steadily diverged. At the same time, it's limitations have been exposed more and more.
In my view, Zig is aiming at this space i.e. where the developer is primarily interested in what the machine is doing. What they have done is kept the C model (largely) but mitigated or removed some of the egregious failings of C.
Zig may not be unique in doing this but it's definitely quite rare. Rust, Go, Swift et al aren't attempting to do this. This isn't a criticism just a perfectly legitimate difference of priority.
As I failed my soothsaying exam, I'm in no position to predict which, if any, will succeed. I hope (without much justification) that having language diversity will encourage natural selection.
Zig is a C replacement: a dead simple language for low-level development, partly disregarding memory safety (there seems to be some improvements, but only where it doesn't make the language more complex).
Could you ever imagine writing something like Tiny C-Compiler for Rust? C is like fancy assembly. Zig seems to fit into that niche quite well, but doing it in a more disciplined and modern way.
To elaborate a bit:
Right now, the standard library relies on an allocator. The language itself does not. If you want to write your own types and back them up by your own allocator, you can 100% do that today. But that doesn't help you with any of the stuff in the stdlib.
We have work on:
1. A trait for allocation, so that allocators can have the same APIs. https://github.com/rust-lang/rust/issues/32838
2. Swapping out that allocator entirely, wholesale. Tor and Firefox both want this. https://github.com/rust-lang/rust/issues/27389
3. Allowing you to swap out the allocator of stdlib types on a per-instance basis; this almost had an RFC for the needed machinery, but was postponed. Will probably come up again in the coming year after #1 & #2 get resolved.
If you see quick compilation as an advantage Go has over Rust, but want Rust’s robust error checking and you don’t like Go’s reliance on garbage collection, Zig might be interesting.