Try clearing out your /documents/my games/Elemental/Units folder.
This will reset the units back to their defaults.
That should let you choose them again.
When I responded earlier I first tried finding the core Sovs and looked in that folder but didn't see them there or in any other folder (inc. the ones in Program Files and ProgramData) so concluded they were encoded in something else, so deleting that folder you mentioned wouldn't help.
Second, I figured uninstalling would delete every trace of Elemental, accomplishing what you suggested.
We should probably change it so you can't delete the "core" sovereigns.
Perhaps also change the uninstaller to uninstall everything? Or perhaps give the options:
-complete uninstall (everything, no exceptions)
-as above but preserve saved games, custom units (Sovs and troops), etc.
