How is no password more secure than username+password?

It is if you use a shared key.

You have a secure key on your computer, and the other one has one that matches it, allowing a secure, passwordless login. I'm surprised that no one has mentioned this.

This link is mostly about remotely logging into a remote server via ssh, without entering a username and password. I do that all the time when I need to ssh into my leased bare-metal server in another state. Surely, it's possible to do that in your case.

How is no password more secure than username+password?

It is if you use a shared key. Here's the way it works, simply explained.

You have a secure key on your computer. The one that you're trying to log in to has a key that matches it. This allows a simple, quick, and secure passwordless login.

This link is mostly about remotely logging into a remote server via ssh, without entering a username and password. I do that all the time when I need to ssh into my leased bare-metal server in another state. Surely, it's possible to do that in your case.