We have a site that has migrated out of the Matrix CMS. Is there any advantage in changing the status of this site from 'live' to 'archived' (ie caching, system performance, storage etc) even though people will not be able to discover the Matrix version?
There are no performance improvements in changing the status, no.
The assets that make up your site exist in the database and filesystem regardless of their status. Removing the site from your system (i.e. move to and purge from trash) may have some benefit (depending on the sites size and complexity).