In Experience Builder, all widgets add in the builder must be shared with the user to load the experience. If a widget is not shared, the experience is not loaded and the user will get a blank page with error. We can say that widget's share is mandatory. For ESRI, it's "as designed".
In WebAppBuilder, when a widget was'nt shared, the WebApp was loaded correctly without the unshared widget. It was perfect to manage user's rights.
My idea is to have the save behavior in Experience Builder : be able to load an Experience without a unshared widget.
Thanks