We have the same need and we have come up with a workaround using the GeoProcessing widget.
Create a GP tool (based on a python script) which takes a user selected polygon feature as input and copies the feature to another feature class (in our case the feature class is in an enterprise GDB underpinning another WFS in the same webapp).
Publish the GP tool and set up the GeoProcessing widget within the webapp.
Within WAB (at v2.4 - not sure about earlier versions) when you click a polygon feature and then click the three dots at the bottom right of the pop-up you get a menu option to set it as the input to the GeoProcessing widget task.
It's not pretty but it works for us internally. Not sure if it would be as easy in ArcGIS Online.
You can handle the attributes copying over in the Python script or having the user enter them in the widget dialogue.
I agree that a simple copy-paste of a feature/geometry (like you can do in Desktop) is highly desirable!