Cannot enable or disable Mail plug-ins
Eventually I moved my ~/Library/Mail folder to the Desktop, reset mail "to factory settings", then re-imported all messages from the moved folder.  It took about a day, including the backup I did first.

Following the above "reset" instructions involves deleting ~/Library/Containers/com.apple.mail/.  When I was perusing the new ~/Library/* and ~/Library/Containers/com.apple.mail/* setup, after relaunching Mail, there were differences before and after, in particular which items lived in the container and which lived in the real ~/Library.  This may be a clue to a cause, but at least there is now a sledgehammer solution.