There should be a page in MediaWiki namespace or a configuration setting which allows to choose one (or more) category that shouldn't be listed on this special page. In this way, the main category of a wiki isn't displayed in this list anymore.
|mediawiki/core : master||Allow to define exceptions for Special:UncategorizedCategories on-wiki|
Soft-redirected categories should still have a category (not uncategorized): the soft-redirect template should set this tracking category (and should detect those that are not empty in another tracking category for pages needing recategorization fixes).
So I don't think we need an exception for soft-redirected categories (including renamed categories pointing to another one).
On the opposite we should have an internal tracking category for categories that are hard redirected (and optionally have some members) for maintenance, because these categories are hard to visit (pages categorized in a hard-redirected category are showing the category in italic at the bottom of the page, so the detection is already there)