This issue was originally about providing for theme templates that would represent theme callbacks used in .inc files. However, drupal_common_theme() is only ever called once, by system_theme(). We could move drupal_common_theme() directly into system_theme(), and then all the theme functions/templates there too. All the places where these functions are used without a full bootstrap currently have to include system module beforehand.
Once they're in system module, there's incentive to factor them back out again.
Original issue by steveoliver
Drupal currently has no way of supporting templates for theme implementations defined in core/includes/* except by searching in themes/ directories
In our effort to replace Drupal's theme functions with [Twig] templates, we need a way for the theme system to find templates for theme implementations in /core/includes/.