Currently Drupal supports the arbitrary creation of URL aliases, stored in the url_alias table. This is not really appropriate for the configuration system. It is not uncommon for there to be thousands of aliases in this table, and the config system doesn't offer the queryability that would be necessary to make this efficient. However there is some argument to be made that this is not actually configuration at all. In core, these aliases represent a 1:1 relationship between a URL and a piece of content. ('about' -> 'node/123'). In this case, shouldn't this information be stored with the node? I think there is a strong case to be made that aliasing should be moved into the entity system, and the arbitrary alias creation at admin/config/search/path should be removed entirely.
There are other types of aliasing that are appropriate for the config system (like pathauto url patterns) but until pathauto is in core that's not really under discussion for this purpose.