But RecoverySafe is just preventing things like "your binary heap was only partially heapified" and not "your heap is now full of uninitialized memory". You can get poisoned values out of mutexes just fine, so everything needs to put itself in a memory-safe state if a panic occurs.
One can bypass RecoverySafe in safe code with the AssertRecoverySafe wrapper.
It does however turn out that safe code in Rust is generally quite exception-safe by default. This is because safe code can't do anything too dangerous, panics are generally only caught at thread or application boundaries (so data that witnesses a panic is usually well-isolated) and there's way less places that can unwind compared to "override everything" C++. But exception safety is indeed something unsafe code needs to fight for (see the aforementioned binary heap in std).
Also take a look at things like the design of the Drain iterator- the stdlib is definitely (intended to be) exception safe.