Detecting when the base layer has changed (e.g. from clicking in a Layers control) is harder than it should be.

The Layers control does not define the order in which it adds and removes layers, so input that changes the base layer may result in a layeradd event followed by a layerremove event, or a layerremove event followed by a layeradd event. This means that any handlers that are bound to either or both events cannot assume that the map has exactly one base layer. It may have zero, one or two depending on the order of events.

I suggest that the Layers control trigger a baselayerchange event on the map after responding to input that changes the base layer. This event would be triggered after the other layer events, and it would include a layer property set to the resulting base layer.