Why, though?
Perhaps it's unfeasibly complex? But if that's the argument, then that's an argument that needs to be made. The paper sets out to refute the idea that C++ already has the information needed for safety analysis, but the examples throw away most of the information C++ does have, without explanation. I can't really take it seriously.
1. Complexity. This manifests as compile times. It takes much longer.
2. Usability. Error messages are poor, because changes have nonlocal effects.
3. Stability. This is related to 2. Without requirements expressed in the signature, changes in the body change the API, meaning keeping APIs stable is much harder.
There’s really a simple reason why it’s not fully feasible in C++ though: C++ supports separate compilation. This means the whole program is not required to be available. Therefore you don’t have the whole program for analysis.
Trying to establish proofs that the pointer is one way or the other can't work, because the pointer doesn't have to be only one or the other.
The fact that you then have to treat the pointer one way or the other is a problem; if you reduce the allowed programs so that the pointer must be one of the two that's a back-compat hazard. If you don't constrain it, you need to require additional information be carried somewhere to determine how to treat it.
If you do neither, you don't have the information needed to safely dispose of the pointer.
The entire point of having a static-type-system, is to enable local reasoning. Otherwise, we would just do whole program analysis on JS instead of inventing typescript.