Yes, you can share your screen in zoom and skype.
At first, I wanted just to play "a funny" video over the webcam (instead of my face), for my colleagues.
And sharing the desktop over the webcam was just a "nice to have" feature, in the case, the application does not support screen sharing.
Screen share in Zoom normally takes up a lot of space and is annoying in my opinion if it isn’t by someone leading a meeting. It isn’t naturally via your webcam.