Members App - Can You Add a Restricted Tag to a Directory?

hi - I'd like to have an entire directory, the page and all it's subpages (even new ones as they are created by content editors) restricted by a tag. Is that possible? I thought protecting the top-most page above subpages protected ones below it, but it doesn't, you need to manually add the restriction tag to each page.

Please let me know if I'm missing a method for this.