You mean, as opposed to the other transparently copyable heap-allocated objects such as ... std::vector, std::list, std::unordered_map, std::string, ... basical

You mean, as opposed to the other transparently copyable heap-allocated objects such as ... std::vector, std::list, std::unordered_map, std::string, ... basically most of the standard library other than the smart pointers? The problem is already there, Box wouldn't change anything.