To log in and administer it? There's even an example; search for "extlinux --once". (There are other options, like a web UI or non-root SSH, but that's the obvious thing. Also if you want to advocate non-root I'm going to want to hear a threat model.)

You don't need a private key on the host for that, only your public key in authorized_keys.

Edit: Oh boy I should have paid more attention. Those are the host keys. :facepalm: