I see zero problem with using SSH, which happens to be a pretty secure protocol. In fact I would prefer it to HTTPS since it is not by default vulnerable to malicious CAs. Note for example that GitHub allows Git access over SSH.

When the author says that the system "exposes the private key", well, it's by design that the user can see it - since they need to use it to identify themselves to the SSH server. It's not much different from being assigned a password by the server. What could be improved is if it was transferred over HTTPS rather than HTTP, and of course also the install script.

(I only speak about the usage of SSH, it's possible that they still do something insecure..)