The right-hand-side blue tabs are fine for listing a couple layers, but they obscure map area and fail entirely for large lists of layers. Most GIS call this capability the "Table of Contents" and it lists the layers present in a map. Typically, the TOC is also used to let the user change attributes about each layer, such as z-index, symbol color or marker, line color, projection etc. Such complicated UI elements obviously don't fit well in the current tabs.
For a next step forward in OpenLayer's TOC technology, let's simply move the tabs into a separate div that can be "collapsed" to save space. It need not do more than just list the available layers and let the user turn them on/off. It should allow a large number of layers, let's say 20 as a good initial target. It should have a visually pretty "closed" state and a usable "open" state.
A next iteration of this might allow layers to be grouped, so that a new layer can be added to a group of existing layers, and all of them turned on/off at once. Such a group might also have the property that only one layer in the group is visible at a time. This would allow, for example, the most recently added layer to be the only active layer in a group.