Unlike a clip, a live input has no width and height of its own. The width and height change depending on the resolution that you capture with it.
So when a live input gets (re-)loaded, we have to check what resolution it is in order to show the captured image at the correct size. This overrides whatever changes you have made to the width and height.
The best way to resize a live input is to leave the width and height as they are, and just use scale instead.