This has been recognised as the next important milestone for Rust and there's work towards making it happen. The details are uncertain yet, because move constructors are a big change for Rust (it promised that address of owned objects is meaningless, and they can be simply memcpy'd to a new address).
The Rust folks want a more usable Pin<> facility for reasons independent of C++ support (it matters for the async ecosystem) and Pin allows objects to keep their addresses once pinned.