I have picked private fields as an example of feature that is needed because it is very simple. You're right that you can build an analyzer (with additional code annotations) to support that, but it's only one example.
Take another example: unsafe traits. They are fundamental to some safety encapsulations, most famously concurrency (`Send`/`Sync`). Here you cannot just build an analyzer to mark something unsafe, because Zig has no traits, its generics are duck-typed.
You can, of course, add traits. But at this point you're essentially creating your own language that compiles to Zig, with all problems this entails (e.g. bad ecosystem support). It's also hard to claim that Zig can be memory safe then.