There is not much we can change for the Google or Bing maps setting, but the Open Street Map offers various layers. For example, adding &layers=C to the OSM URL brings up a cycle map, &layers=P some nice variant of the standard map, and there are also the layer types H, T and Y available. In all cases it is enough to just append the &layers=$ part to the URL. Maybe the option could be added to the miscellaneous section in the preferences, where users could pick one of the layer options from a menu, or type the &layers=Y part by themselves, to change the default OSM map style?
Can already be done in Preferences / Miscellaneous / Advanced: [Behavior] image_locate_services.
Thanks, Alex. It works.