You always know the actual dynamic type at construction time, how would you otherwise construct it?

> For example shared-ptr to base can correctly invoke the correct derived type

Invoke what exactly? Im sorry I don't understand what you're trying to say here.

I guess you can force all derivied types to implement a clone() function, such that box<T> can do the deep copy, but Id consider that a fairly big inconvenience for such a simple pointer type.

No need for T to have a clone function. You can use standard type erasure techniques. Consider how std:: function or std::any is implemented.