Looks like it depends on the specific operation(s) you want to perform [0]. For instance, constructing a std::polymorphic<T> from an object of type T or derived from T requires that that object is copy-constructible (among other requirements), but copy-assigning one std::polymorphic<T> to another only requires that T is complete.

[0]: https://eel.is/c++draft/polymorphic

Yes, there is currently no move-only std::polymorphic, like there is a move-only std::indirect ...