Say I don't care about the sanctity of my commit history, and wish to scrub my personal email from all of my public repositories. How would I go about doing this without losing the commits themselves?
Then you have to force push.
Note, you will still have the same number of commits in the same order with the same diffs, but they will be new commit ids.
You’re “rewriting” your history. Which in the case you outline is perfectly fine. But note, anyone who’s pulled down the branches you’re changing will need to reset rather than pull your changes otherwise git will attempt to MERGE the new history with the old one.