Earlier quoted context omitted.
Private commits aren't immutable at all. You can change anything about them up until you push them to a remote repository that other people are syncing from. I routinely squash a bunch of private commits together before issuing a public PR, for example.
Commits are immutable; when you squash commits you're replacing them with new ones and rewriting the history. And since there is no difference between your local repository and the remote one, the reason why you wouldn't squash commits on the remote repository is to be nice to your coworkers. So unlike PR's, if your coworkers criticize your commit messages it's already too late.
Uhh, there's plenty of difference between your local repository and the remote one. One is local and used just by you and one is remote and used by many, for starters. Changes aren't automatically synced between them. You can rewrite commits locally to your heart's content (which I do all the time). You aren't "locked in" to anything until you've pushed it to a shared repository and someone syncs from it.