the layerlist should have an "Only" option next to each layer, like by Airlines on SkipLagged.com. So it turns only that layer on and shuts others off. And perhaps the radio button idea others have proposed as well.
Again and again the problem with viewers is too many layers on, slow and confusing to users. Also needs partial checkboxes like ArcEarth to indicate only some layers in a parent group are on.
This is is one of the most visible things to end users for Esri's entire product portfolio- how the layerlist works.