Sounds good to me! @neil can you add that to your list for next week? Perhaps an admin setting named edit_history_visible_only_to_staff or something similar.
Just so everyone knows, you can already see “was this edited” and how many times it was edited at the upper right of each post, like so:
The pencil will be redder if the edit was recent and the total count of edits.
That part won’t be changing, it just won’t be clickable if you are not staff (or the owner of the post, I guess).