I have a Shape class containing potentially many vertices, and I was contemplating making copy-constructor/copy-assignment private to prevent accidental needless copying of my heavyweight class (for example, passing by value instead of by reference).
To make a copy of Shape, one would have to deliberately call a "clone" or "duplicate" method.
Is this good practice? I wonder why STL containers don't use this approach, as I rarely want to pass them by value.
Restricting your users isn't always a good idea. Just documenting that copying may be expensive is enough. If a user really wants to copy, then using the native syntax of C++ by providing a copy constructor is a much cleaner approach.
Therefore, I think the real answer depends on the context. Perhaps the real class you're writing (not the imaginary Shape) shouldn't be copied, perhaps it should. But as a general approach, I certainly can't say that one should discourage users from copying large objects by forcing them to use explicit method calls.