Moving pages in the Page namespace as a non-admin (or non-bot, depending on local suppress-redirect perms) is rather fraught, as the redirects block other pages being moved into places. The normal workflow is to ask an admin.

A separate permission for suppressing redirects specifically in the Page namespace would allow general users to re-arrange the pages as they need. Projects can make their own decisions about which user groups include this permission (e.g. autopatrollers, a separate group, etc etc).

This would then feed into a separate task for an on-wiki way to move these pages effectively.