Just don't fall into the trap of believing that only making constness transitive would make it fool-proof.

A non-"pure" const member function with const parameters could still call some other function with access to a "mutable" alias to what you have a const reference to. You would need something more, such as an ownership system to make the compiler make that impossible (as in Rust) or to detect it (the topic of Master's thesis, BTW ) ... but then it would no longer be something resembling C++.