For folks using several installations for example for development, staging and live sites, plugins often use the same settings for each installation. Where you ideally want different settings for the different environments, it becomes much simpler if it can be handled by the plugin, rather than through various workarounds.
I'm thinking that perhaps one ID pair could be added to the plugin for each related installation, and maybe that idea could be extended to the configuration being connected to the ID pair.
One example of it in use would be with the wpengine.com staging option. They have a close to one-click option to move a staging site to live. Of course if the Clef plugin on the staging site has the ID pair for the live site, you can't actually use Clef to log in to the Staging site*. If it has the Staging site ID pair set up, then when you move it to live, nobody will be able to login until you go in to the Clef configuration and update the Clef ID pair to be the Live settings.
*There is the workaround of entering the two application domains, but it appears that allows login, but doesn't work for the single signout. Also it doesn't allow for differing access requirements between Staging and Live.