Often, when 'Remove Selected Local Overrides' isn't possible, selecting 'Remove All Local Overrides' will replace parent page text boxes, thereby deleting any content you may have (and may have spent a lot of time working on). Restricting removing all local overrides to a selected or unlocked layer would allow all other content on other layers to be protected.

ps Reapplying a parent page as a workaround has the same effect – parent page text boxes are replaced.