I think this is the point that's often overlooked. Everything in safe rust is supposed to be both memory safe and thread safe. The textbook implementation of linked lists and trees are not thread safe, and easily not memory safe.
In practice this often reduces to the same thing, but you can still create deadlocks, etc.
Also, as a sibling comment points out, the "thread safety" guarantee is relatively narrow -- it won't guarantee a general lack of concurrency bugs any more than a gc will guarentee reasonable memory usage.
I haven't thought through the details, but I suspect it's possible to adjust the semantics of rust in a way that allows multiple mutable references without sacrificing memory safety.
What you would hit is that the compiler would be hindered when doing optimizations in the same way that c and c++ compilers are, because of pointer aliasing.
There's a trade off there, and I think you can make the argument either way.
Same with Send, which is more primitive than Sync.
Please do think about the details deeply, because if you find a way to do this, you'll probably bring a revolution to Rust.
I'm kind of skeptical of course, but I'd be really happy to be wrong.