This would probably be more appropriate as a plugin rather than a core feature but I wonder if an auto-flag might remove that trade-off.
Essentially working the same way as auto-bump does now but flagging rather than bumping to hide it from anyone who isn’t involved in that housekeeping.
Of course that may involve trading minor confusion/inconvenience in the community with making it more awkward for moderators to deal with other flagging unless there is some good way of filtering out those housekeeping flags.