The biggest problem is that there's some awkwardness around RAII; I'm not sure whether that could have been avoided with a different approach.
Of course, ideally you'd want it to be compatible with the standard-library APIs that allocate. This is implemented, but is not yet at the point where they're sure they won't want to make backwards-incompatible changes to it, so you can only use it on nightly. https://doc.rust-lang.org/stable/std/alloc/trait.Allocator.h...
Or are you suggesting that the choice of allocator should be dynamically scoped, so that allocations that occur while the bump allocator is alive automatically use it even if they're in code that doesn't know about it? I think it's not possible for that to be memory-safe; all allocations using the bump allocator need to know about its lifetime, so that they can be sure not to outlive it, which would cause use-after-free bugs. I'm assuming that Odin just makes the programmer responsible for this, and if they get it wrong then memory corruption might occur; for a memory-safe language like Rust, that's not acceptable.
I've never used Odin, so I don't know whether/how they'd keep it safe.
[0]: https://docs.google.com/document/d/1243br9VVluZN0ZD9MVKSQMAw...
On the other hand, if you required an API along the lines of bumpalo::boxed, and also were willing to add a bit more runtime overhead on top of that (for the tracking bits and the allocation count), then this could be done in Rust as a third-party library. Each executable that transitively depended on it would have to opt in with #[global_allocator], though. Also, I personally would rather have an API where the compiler makes sure I don't screw this up, than one where the runtime crashes my program if I do; this is generally a common sentiment in Rust, and points towards a bumpalo-style API.
Edit: Spelling. PS: Though might also be an awesome way to shoot yourself in the foot.