Currently Zig has the same issues as Rust in this context, primarily depending on a compiler that's too complex for a single person to maintain if necessary.
But in Zig's case it seems there's a pretty good chance that will change if they're able to drop LLVM in the future.
You can create and link to shared objects and create statically or dynamically linked executables. What more could you want on "embracing binary distribution"?
